If I have a co-borrower, do we have to split the mortgage deduction? Or can one of us claim the whole thing?

You must "split" the deduction if you file separate tax returns. Each of your will deduct your paid share.

 If joint account and even amount, you would simply split 50/50. 

If we split the deduction, my partner's half would be less than the standard deduction, so he would end up taking the standard. Does that still mean that I can't claim the entire house, since he wouldn't be deducting any of it?