In order to claim the mortgage interest, two criteria must be met.
1) You must be legally obligated to pay it.
2) You must have actually paid it.
So paying it from funds in a joint checking account, you'll have to split it 50/50.
Same holds true for property taxes unless one of you can prove (if audited) you paid more or less than 50%. With funds coming out of a joint account, that's almost impossible.