No. The rules about splitting certain child dependent benefits only apply to parents who are divorced or separated and live apart and share custody. When you live together with the other parent, only one parent may claim a child as a dependent. The other parent should leave them off their tax return entirely.
However, if you have three children who qualify as dependents of both of you, you don’t need to go all or nothing. You might maximize your advantages if you claimed 2 and 1 or 1 and 2.