No-one's posted for like, ages, but this looks like an interesting thread. I once had a conversation with a German where I was speaking German and he was speaking English. And another one the other way around. But both times I did notice that we were speaking different languages.

And a kind of Anglo-French conversation once, but neither of us understood the other, so...

Not really, unless you count the occasional Franglais conversations that sometimes take place in my house (we're all native English speakers) and the time I tried Welsh out on my monolingual English-speaking classmate in math. The latter situation sounds pretty ridiculous because it was; he kept saying he'd invented Welsh and such silly things, so I felt like I had to disprove his supposed knowledge of it.