A person can deduct mortgage interest as long as that person's name is on the title or deed and he/she actually paid this interest during the year. So if you both pay half the mortgage each month, then you can include half of the mortgage interest on each tax return. If the funds are paid through a joint account then you can choose who takes the deductions (as long as the total adds up to the total being reported on your Form 1098) or allocate the amounts how you deem appropriate.
If you live in a community property state (Arizona, California, Idaho, Louisiana, Nevada, New Mexico, Texas, Washington, or Wisconsin), you will want to divide the 1098 deductions 50/50.)
Please note that if one spouse is claiming an itemized deduction, the other spouse must also itemized on his/her married filing separately income tax return. So if you itemizes deductions, your spouse cannot claim the standard deduction.
Here is some additional information about married filings separately :