Legal Question in Family Law in Illinois

Assuming you mean can your ex stop supporting HIS children just because you remarried, you need to look at the divorce decree, which should specify your ex's obligations are toward HIS children. Your new husband certainly is "responsible" as any husband in terms of the relationship you and he have, but if child support from the ex is still mandated, you can't artibrarily trade one obligation for the other. If I was the ex and the divorce decree let me off the hook, I'd want to run into court and get an order confirming that. Otherwise you may have to go to court to enforce the child support portions of the decree against him if he doesn't voluntarily resume them.

If your ex has custody of the children, as you seem to imply, then your new husband's income is not attachable by your former husband for child support.