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I believe the most accurate word you'll find for the conversation itself is "bilingual." As in:

The two ladies were having a bilingual conversation

However the inability of the two speakers to fully command both languages is a property of the speaker, not the conversation. The term for this inability is "receptive bilingualism." You would need to change up the syntax a bit to clarify the situation:

The two ladies were having a bilingual conversation, however both were only receptively bilingual in the other's language.

"Passive speaker" is another way to refer to this type of speaker, however this could also imply that the speaker is simply non-aggressive in their speech.

One term that comes up in this context is cross-language (or cross-linguistic). I haven't found a formal definition for this term, but it is fairly transparent. It collocates with "mutual intelligibility" (see below) but also appears in contexts where, for example, the participants in the conversation are employing an interpreter. A couple of examples of use (bolding added):

[W]e aimed to assess the cross-linguistic intelligibility between the related languages as it is in actual practice, i.e. including the effects of the participant’s education. Our study therefore offers an overview of the cross-language intelligibility between related languages . . . .

—Charlotte Gooskens, Vincent J. van Heuven, Jelena Golubović, Anja Schüppert, Femke Swarte & Stefanie Voigt (2018) Mutual intelligibility between closely related languages in Europe, International Journal of Multilingualism, 15:2, 169-193, DOI: 10.1080/14790718.2017.1350185

People using Skype or web applications can now have a cross-language conversation, each speaking in a different language.

—"Real-time Speech Translation in 23 Languages for Business; ReadSpeaker Adds Text-to-Speech Voices to Translate Your World's Voice-to-Subtitles Software", Monday, November 26, 2018 (press release)

Another potentially relevant term is mutual intelligibility. From Wikipedia:

In linguistics, mutual intelligibility is a relationship between languages or dialects in which speakers of different but related varieties can readily understand each other without prior familiarity or special effort.

Note that in linguistics "mutual intelligibility" generally¹ refers to inherent characteristics of the languages, rather than special knowledge on the part of the speakers—that is, it's usually used for related language "pairs" like Portuguese and Spanish or Swedish and Danish,² but generally wouldn't be applied to, say, an English speaker who knows some Mandarin and a Mandarin speaker who knows some English speaking to one another in their own languages.

With that caveat, I think the adjectival form, mutually intelligible, could be used for your situation. The plain meaning of the phrase is fairly transparent and would seem flexible enough to encompass the English/Mandarin situation described above, particularly as it is also used in non-linguistic contexts to describe communication and conversations. Some examples of use, both technical and non-technical (bolding added):

"Are Urdu and Sindhi mutually intelligible languages?"

—Yahoo Answers question (opinions in answers are mixed)

In my experience of observing Spaniards and Italians talking in their respective languages to each another, it is possible for them to have a mutually intelligible conversation as long as they speak clearly.

— Conor Clyne, "How different or similar are Italian and Spanish?" Tsar Experience, August 25, 2016 (blog entry)

Whatever the differences between the Stoics and the Christians, they can be put into mutually intelligible conversation.

—Christopher Kavin Rowe, One True Life: The Stoics and Early Christians as Rival Traditions, 2016

So for your example, you could say something like

• They were in a bus and had a mutually intelligible, cross-language conversation.


• They were in a bus and had a cross-language conversation.


• They were in a bus and had a mutually-intelligible conversation in Urdu and Sindhi (respectively).

¹_{"Generally" only because I've seen some suggestion that sociolinguistics occasionally use it in a different sense.}
²_{See the May 28, 2014 Language Log post "Mutual intelligibility" and especially its comments for an informal discussion of the degree of mutual intelligibility of dozens of language pairs.}

It has been called code-mixing in academic papers.

Code-mixing is the mixing of two or more languages or language varieties in speech.

Wikipedia

There is a concept of diglossia.

The use of two markedly different varieties of a language in different social situations, such as a formal variety at work and an informal variety at home. [American Heritage]

Usually this term is used when the same people are speaking both languages (e.g. people who speak an official form of the language in formal occasions and a dialect the rest of the time; or else speak English at work and another language the rest of the time).

By stretching it a little, we could also call this particular situation (where individuals speak a single language but understand two) as a case of diglossia?

In this particular case there does not seem to be any high or low language, but simply two persons from different backgrounds speaking different languages (hence it is a situation of multiculturalism) but sufficiently familiar with the other language that they have a passive knowledge of it.

What is interesting to guess, is how this situation might evolve in time: by one language supplanting the other? Or a fusion of the two, similar to what happened to Middle English? Or a third language (as English) taking over?

I am a translator and interpreter and speak four languages (I am quadri-lingual, in fact). There is no specific term for this. And it's certainly not bilingual.

If this refers to two people, it just means they at least passively know each other languages but actively only use their own. They each have a passive knowledge of the other's language, otherwise they'd be speaking one or the other. They are passive "speakers" of a language. passive speaker

Passive knowledge means you can understand a language or read a language but cannot actively speak it with any confidence. For example, in my case, I speak three Romance languages but do not actively speak Italian. However, my passive knowledge of Italian is very good so I can actually carry on a conversation with an Italian speaker if they can understand English. (In fact, I can carry on a simple conversation but can understand an advanced one passively.)

But beware: In the world of translation and interpretation, a passive language has a more technical meaning: it means the language from which a translator or interpreter is working. This is often symbolized as: German>English, English>Chinese. If a person is bilingual (which is not as frequent as one might imagine), this is signified like this: English<>Chinese.

Here is a blog post about this issue as regards active and passive vocabulary in language learning, though it applies to monolinguals as well. passive and active vocabulary

I often speak English to my husband and he responds in Spanish. We have a conversation in two languages.

Bilingual means an individual can speak two languages equally well, though there are different levels of bilingualism. And, if I hear someone say: "We had a bilingual conversation." I would understand that each of the speakers spoke two languages and both switched back and forth between those two languages without causing a break in their conversation due to lack of understanding.

As for codes, mixing and switching them is not "inter-lingual". A speaker code switches within her or his own language.

Reading over the answers, I had to laugh when thinking about having a conversation with someone where one person uses a different language than the other and they understand each other. Of course, they understand each other, otherwise it would not be a conversation, would it? And, I daresay that mutual intelligibility is an issue that does not involve more than one language necessarily. Who hasn't had a conversation with eggheads in a monolingual situation where there was no "mutual intelligibility" at all?

And for the record, the idea that a Spanish speaker can understand a Portuguese speaker is a very specious idea. The fact much in the two languages is very similar does not account for the parts that are completely different. And this can lead to major misunderstandings and comical situations. (I just can't think of an example at the moment, as I write.) The mutual intelligibility factor is true only to a limited extent.