Multiple parts to this. We share a house and split the mortgage payments. Assume everything as would be in a typical married family but unmarried. Both children are ours.
sorry, but it may be improper for each of you to claim 1 child under the tax rules
since you are both the parents
apparently, you live together for the whole year then
the IRS says it's the parent with the highest AGI that's entitled to claim them.. so if you both filed as head of household claiming one child you both misfiled. one gets both the other files as single.
some states recognize a common law marriage - but most require that it be recorded.
you need the help of a tax pro because there are significant penalties for claiming tax credits you are not entitled to.
edit: basically trying to decide if for tax purposes its actually more beneficial to remain unmarried. Have similar incomes, within 25%.
The "higher AGI" rule only applies if both parents claim the same child. You can each claim one child, or either one of you can claim both children, as long as you don't both claim the same child.