As long as you both are on the deed - either of you may use property tax and mortgage interest deduction.
Generally - each of you may deduct the amount you or he actually paid. If some payments were paid from community funds - each of you entitled for 50% deductions.
If you have separation decree - that document may specify who is entitled for deduction and in which proportion.
Please let me know if any clarification is needed.
Tax deductions are taken by the person who made payments - that is the IRS's point of view.
If you made rental payments - they are not deductible.
If you think that you are entitled to deductions - you try to negotiate with your partner - if you would not come to any agreement - the only way - to go to the family court and get a separation decree.
The separation decree signed by the judge may specify who is entitled to deduction and in which proportion.