Are you on the deed? If so, then yes, you co-own the house. Do you have a separation agreement stating otherwise? If not, then you may co-own the house. Are you in a community property state?
There are a lot of possibilities, but if you are on the deed and paying the mortgage out of a joint account, then yes, you would co-own the house.
If you are itemizing and were still legally married on the last day of the year and filing a separate return, both spouse must itemize. You would split the mortgage interest and property taxes if you both own the house. Any medical expenses, you would deduct would have to be your own medical expenses as would state and local income taxes. Medical expenses are only deductible for the amount that is in excess of 7.5% of your AGI.
If filing separately, your standard deduction would be $12,950. (But again, you both must either Itemize or take the standard deduction.) So, you would only benefit from the mortgage interest if your total itemized expenses are greater than $12,950.