You have one combined household, so only one person can be the "head" of household for tax purposes. That is the person who pays more than half the total household expenses. Total household expenses includes rent or mortgage, utilities, insurance, repairs and maintenance, property taxes, and shared food, but does not include personal expenses like clothing and medical care.
It sounds like you did everything correctly, and there is nothing you can modify to improve your position. Your only other option would be for the BF to claim all three children, which would force you to file as single, and the BF probably must still file as single as well if he does not pay more than half the household expenses. In rare cases, he might get a tax benefit (like EIC) that is more than the tax benefits that you would lose, so the only way to know for sure is to test the possible combinations. You can't ever claim your BF's two children unless you either get married, or he is not a "taxpayer" (meaning his income is enough that he does not file, or he owes no tax and only files to claim a refund of withholding and claims no other dependents, deductions or credits.)
