When you file as married filing jointly you file one tax return for both of you together. A dependent on your joint tax return is not claimed by one or the other of you. The two of you jointly claim your dependents. It doesn't matter which one of you is the biological parent and which one is the stepparent. You just list all the children on your joint tax return.
What may change things is if the children live with other parents sometimes.
As discussed, on a joint return, you are your spouse are considered "one taxpayer". You report all your combined income, deductions, credits and dependents.
Also, a step-parent has the same legal rights to claim a dependent as a biological parent. So even if you filed separately (which is usually not recommended) then you could divide the children and stepchildren in any way you wanted to.
The only time this will change is if any of the children live more than half the nights of the year with the other biological parent. Then we need to do some more digging.