Translation:Are we waiting for my wife or your husband?
I strongly disagree that "woman" and "man" is not accepted as a correct answer. It does make sense.
Would "do we wait for....etc." be correct here as well or does Czech have another type of verb construction for that?
I believe it is more of an English issue. Can you imagine this sentence in any other tense than progressive?
With "X or Y" as object it sort of implies that the question is about the choice for one of them. I can imagine though that you can ask: "Do we wait for my wife or your husband or do we go out and do the groceries ourselves"? The meaning shifts: the waiting itself is now in question, not in progress.
For the choice between waiting or grocery shopping you would structure the Czech sentence differently. BUDEME čekat na tvou ženu nebo mého muže nebo půjdeme nakoupit?
The Czech ČEKÁME is happening now
Can we also change the waiting in this case? Because I said 'waiting on" and the correct answer was "waiting for."