Both of you cannot claim HoH. Although that's theoretically
possible, you situation does not qualify.
You say you split expenses evenly. That would mean neither
of you can claim HoH, as neither has paid MORE than half the household
expenses. You need to arrange your finances so that the person you want to be
HoH pays slightly more than the other. Remember, to be HoH, you must be
claiming a dependent that resides in the household. So, it sounds like that
should be you.
