Yes, if two unmarried people share a home with their two biological children, each taxpayer can claim one child. However, only one person can be head of household, that would be the parent who pays more than half of the total household expenses. The other parent would file as single with one dependent.
What is actually best is complicated, and you may want to test different combinations. How you report the children will also affect the child care credit or flexible spending account use, if you have that, and will affect EIC, if you qualify.
