No. In order to claim anything pertaining to the mortgage payments, you must meet two basic criteria.
1. Be legally obligated to pay it.
2. Actually pay it.
If you have a formal rental agreement (which I doubt, since this is your fiancee') then rent you pay would not be deductible on your tax return, and the landlord would be required to report the rental income on SCH E as a part of their own 1040 personal tax return.