I live with my boyfriend, we have a child together and then I have a child. We split out bills even and beyond that I pay over 50% to care for my daughter as her father doesnt pay support. Are we both able to claim head of household with him using our child and myself using my daughter?

“Are we both able to claim head of household with him using our child and myself using my daughter?”---->Yes, as long as both of you can satisfy the HOH requirements; To file your return as HOH, you should satisfy several requirements; as of December 31 of the tax year, you were unmarried or legally separated under a separate maintenance order issued by a court; your child, adopted child, stepchild lived with you more than half the year. The child between you and your boyfriend can qualify as your or your boyfriend’s qualifying child. You( or your boyfriend) paid more than half the cost of keeping up a home for the year.
Taxpayers claiming the Head of Household filing status benefit from a higher standard deduction and lower tax rates compared to the single filing status.
Please visit the IRS website here; Publication 501 (2010), Exemptions, Standard Deduction, and Filing Information