I’M MARRIED FILING SEPERATELY. WE HAVE A HOUSE, BUT THE MORTGAGE IS UNDER HUSBAND’S NAME. WHAT DO I ENTER (A RENTER, HOMEOWNER) ON THE NJ HOUSING SITUATION SECTION?

You do not have to be on the mortgage to be a homeowner.  If your name is on the deed you are also a homeowner.  If your name is not on the deed you can select other if it is available.  If it is not available then you would choose homeowner. You are not a renter.