Each person may only be claimed as a dependent by one taxpayer, assuming that they qualify of course.
Also, only one of you can file as head of household. To file as head of household, one of you must pay more than half of the household expenses, and claim at least one qualifying person as a dependent. The other one would file as single, and can claim some of the dependents however you decide to split them up. If you pay exactly half of the household expenses each, then neither one of you can file using head of household. I think it is unlikely that you pay exactly half, it only has to be $1 difference.
