Generally, courts are only going to look at the income of the mother and father in determining a child support order. The idea of child support is to put the child in a financial situation that is similar to what would exist if the parents had not separated. A step-parent has no legal duty (in common law or in most state statutes that I know) to support the child of their spouse, other than an adoption.
Now in reality, what can happen is that banking accounts and taxes can be seized to pay past due child support that the husband owes. If the husband and his wife file taxes jointly a state child support agency will seize any tax refund if an arrears is owed. The wife can file an injured spouse claim, though. With bank accounts it can get trickier to prove who owned what money, to prove that the money belonged to the wife and not the husband. But, it can be done.
In the end, it's highly unlikely that a court would force a new spouse to pay for a child that isn't theirs.Ask a similar question