I don't think the IRS would agree with your approach, unless you actually paid for all the interest and property taxes and your housemate paid none.
Refer to https://www.irs.gov/faqs/itemized-deductions-standard-deduction/other-deduction-questions/other-dedu...
Each of you are only entitled to deduct payments you each made. You can not deduct payments she made and she can not deduct payments you made.
