You need to file for child support yourself. His comment of Joint custody is meaningless. It sounds like the children live with you, so you have physical custody and that is all that matter. If HE not his mother has the children for 90 overnights within a 12 month period then he does get a credit in the form of the "shared" custody guidelines as opposed to the "sole" custody guidelines. So if he is refusing to pay anything go file for child support today.
Do not go to DCSE, go to the Court house or hire an attorney to file now before he leaves in January. Have DCSE enforce the order later but dont wait.
I agree with the previous attorney's advice. You should immediately file for custody, visitation, and support. If after the petitions are filed the parties come to an agreement then that agreement can be entered as the Order. You husband owes a duty of support to the children. Even if the two of you agreed to exercise 50/50 custody it is still possible that he could owe support for the children. That would be dependent on the incomes of the parties.