It's very common to use a get-passive with married:
My wife and I have been living here since we got married.
Most passives use be, but other verbs are possible as well: Pullum lists come, get, go, have, hear, make, need, and see. Most of these are relatively uncommon and each one has idiosyncratic rules for when it's appropriate. In this case get is appropriate because of married.
Your active version ("since we married") sounds less common but I think it's also acceptable. Your perfect be-passive version ("since we have been married") doesn't sound idiomatic to me, and I would avoid it in this case.