If you are the owner of the house and you pay the interest, then you can deduct the interest. If part of the interest during the beginning of year was paid by your former spouse, you can only deduct the amount you paid.
You said mortgages, as in two or more. If you have a home-equity loans, remember that starting this year, only interest on acquisition debt is deductible. The interest on equity debt is not deductible. Acquisition debt is debt used to buy, build, or substantially remodel your home.