Can mahr be a payment towards a house for the bride to own?

Yes, it can. But you need to be very clear about what's being given as the mahr.

Is the mahr being given as the entire home?

Is the mahr being given as the value of the down payment only?

Is the mahr being given as the down payment plus part of the ownership of the home?

Meaning you and your husband would partly own the home 50/50?

And if so, when you divide that value, are you going to get the down payment back first, then divide the rest of the equity 50/50, or are you just going to split it 50/50?

Those are all questions that should be answered.

Why? To avoid conflict later on.

And you might say to yourself I love him so much. I'm never planning to divorce him. I'd be destroyed if I find out he died. Believe me, even when you sell one house to move to another, that issue will come up.

So the clearer you can be about what that mahr will and what it will represent, ownership in the home, ownership in part of the home, or ownership up to the amount of the down payment, needs to be very clear.