My girlfriend and I own a home together. I made $65k while my girlfriend made $56k. She receives rental property income of $10k a year. Who would benefit more from claiming the mortgage interest on our home?

It's a little hard to say who would benefit more only because you didn't mention any other financial info. I'm assuming you and your girlfriend probably have other deductions, adjustments to income, credits, etc. that aren't listed here. Either one of you could conceivably do better than the other by claiming it. For some people, a bigger benefit means a bigger refund. For others, it means paying less taxes. Just run the numbers both ways and compare the results to what you both are looking for. Take care.