As long as you are a legal owner of the property, the person who makes the mortgage payments is the one eligible to claim mortgage interest and property taxes. If you both pay, you would split it between the two of you.
When you enter it into TurboTax, you should mark the box for My name is not on the 1098. TurboTax will ask follow-up information about the person who the 1098 was issued to.
