Since you are a part owner of the property, you are by default obligated to pay the mortgage, so you would be able to deduct your share of the property taxes and mortgage interest. It would be helpful if you actually paid the mortgage, but if you co-mingle funds you may be able to argue that you did that, especially if paid from a joint bank account.
There wouldn't be any depreciation to deal with when you sell the property unless you rented it out. Who paid the mortgage or deducted it on their tax returns would not affect the ownership of the property, so it would not matter when it comes to reporting the sale of the house.
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