No. You are not legally liable for the mortgage interest or any other expenses. Now, your brother can claim what you pay as rental income and report that on Rental Schedule E.
Your brother CAN claim what you pay as rental income, but he is not required to. Instead, you paying his mortgage and real estate tax can be considered you providing support for him.
But, as the other reply said, you are not allowed to deduct those expenses because you are not legally obligated to pay them.
A bigger question is can you really claim someone as a dependent, if they live in their own home.
According to IRS Publication 501:
Person living in his or her own home. The total fair rental value of a person's home that he or she owns is considered support contributed by that person.
Living with someone rent free. If you live with a person rent free in his or her home, you must reduce the amount you provide for support of that person by the fair rental value of lodging he or she provides you.
The IRS has a worksheet that can be used to help with the support calculation. See: http://apps.irs.gov/app/vita/content/globalmedia/teacher/worksheet_for_determining_support_4012.pdf