HOH is a special status for single parents caring for children.
There is no problem filing a joint return. A step-parent has the same legal right to claim a child dependent as a biological parent, so the fact that your spouse is your children's stepparent instead of biological parent has no effect on your tax return.
If you feel the need to keep your finances separate from your new spouse, you may choose to file as married filing separately, although this may cause you to owe more tax, because some credits and deductions are limited or disallowed when filing MFS. If you file MFS, then either parent can claim any children as dependents, or you can split them any way you like, because of the stepparent rule.
