“Is that supposed to be his apartment?”
You're watching a movie about a guy who lives in New York. The character is a waiter at a restaurant, but the apartment he lives in is big and new-looking. You know that New York apartments are really expensive. You say this because don't believe that the character could afford such a nice apartment.
Is that supposed to be his apartment?
This phrase is used to criticize things. When you don't think something is good enough or realistic enough, you say "Is that supposed to be ___?" For example, if someone compliments your hair cut, but says it in a way that actually sounds rude, you can respond:
Is that supposed to be a compliment or something?
Or when someone tries to make a joke, but the joke offends you:
Is that supposed to be funny?
You can use "this" with the phrase as well as "that":
What, is this supposed to be a nice restaurant? If you ask me, it's way overpriced and not all that good.