Please get one of the TAX PROs to answer this one.
Most of the information I know is about claiming the interest. As far as the Outstanding Mortgage Principal, I would put in the whole amount because that is the number the IRS is looking for (and if you both signed for the mortgage, you are both equally libel for the whole amount).
...But what I understand is The IRS will see whomever is on the 1098 as the one who can CLAIM interest and puts in the numbers (including Outstanding Mortgage Principal). I've seen partners figure out who benefits the most and then work out a plan.
I found an article where they noted you can put half the interest with a note pointing to a letter from the other person explaining the situation. Link to Pocket Sense
In any case, I would wait for a pro to answer or get the paid tax advice with audit support.
