"Live at my working boyfriend." I assume that means you live at a home owned by him or leased to him.
"My two children." I assume that means they are not his biological children.
He cannot claim the children because they are not related. So, you can and should claim both of them.
You cannot claim him as a dependent. He makes too much money. He cannot claim you as a dependent, for multiple reasons.
The only real question, on the table, is do you qualify to file as Head of Household (HoH), instead of Single. HoH is very beneficial to you. Head of household gives you a bigger standard
deduction and lower tax rates than Single. The main
requirements for Head of Household are: a taxpayer that
1) is single or did not live with their spouse at any time during the last
half of the tax year.
2) has at least one closely related dependent (usually a child) that lived
with the taxpayer for more than half the year
3) pays over half of the support of the household expenses, including rent
/ mortgage..., food.utilities etc.
The fact that he owns the house or the lease is in his name does not prevent you from claiming HoH, if you still actually pay most of the bills.
