If my parents co-sign on my mortgage, would they be able to deduct mortgage interest on their taxes next year?

Probably not. The interest paid is reported on a form 1098 and it is reported under the social security number of the primary borrowers.

There are circumstances where you can pass the interest deduction on to another party but the deductablility of the interest is going to depend on other factors in their tax return. This is not their primary residence so cannot be deducted as such. Can it be treated as investment interest? I'm not sure. There are limits to investment interest deductions. The question would really need to be discussed with a CPA.

Stephanie, I'm both a mortgage professional and a tax preparer. George below was pretty accurate with his answer of "it depends." The first factor here is whether or not your parents qualify to itemize their deductions; but, the 1098 form will be issued in your name as the primary borrower. It will be up to you to determine what amount of that interest you will deduct and they will deduct. On the Itemized Deduction Schedule A, the mortgage deduction allows for deductions of both a primary residence AND a second home up to $1 million in acquisition indebtedness and a $100,000 in home equity debt; a second home can be anything like a large beach house, a timeshare, a boat that has kitchen and bathroom facilities, etc. Because you won't be renting the home from your parents, this does not qualify as an investment property; however, because you will be living in the home, as a close family member, this typically would qualify the home as a second home for tax purposes. Ultimately, though, this is a question that your parents can only have specifically answered by their tax advisor; another resource for them is IRS Publication 936, Home Mortgage Interest Deduction.