You have a 2nd home, not a rental unit, since he is not paying rent.
So:
1) You do not have to claim it as a rental unit. In, fact, you are not allowed to claim it as a rental unit. It's not optional. Even if he was paying rent, it would have to be fair market rent to qualify.
2) You can claim it as a 2nd home, because that's what it is. You own it and you family living in it. You may deduct the mortgage interest and real estate tax, on Schedule A