He will have to pay housing for you and his children at least until you are divorced. If you are not living on base, the military gives him a monthly monitary allotement to pay for your housing. He may try to keep it. If you do live on base then he will have to go into single dorm housing so you can get a place.
My son actually ran into this issue. His wife was in the military and he was a student and took care of their child. She ran off with another person, leaving my son and grandson. She didn't want to pay at first either. He went through her chain of command and they made her pay the bills until my son could finish his semester and then he moved back home. They have since divorced and worked out a fairly friendly custody agreement. Neither of them pay child support but both work to split their son's cost and to make sure he gets to see both parents as much as possible. So my recommendation is to call his chain of command to at least get the housing allotment.
FYI - she had to send a receipt to her commanding officer every month to show that she had paid the bills. They did not take it out of her check.
Dear Mrs. Miller, Your soon to be ex is going to get a real dose of reality very soon. He has a 18 year obligation he is going to have to honor. The states now cooperate with one in other so you can run but you can't hide. Does he really think the government is going to say "oh sure you don't feel like taking care of your obligations so just let us do it for you." This is not going to happen believe me. Ask for the moon and you might get most of it. You may not even have to get a job in all of this. I pray this has been a real eye opening experience for you. He may figure out he really blew it and want to go back to you. You are young and there is such a better man out there for you just wait and see! He has demonstrated his character and lack of loyality. You do not want this man in your life any longer! The worst thing most of us ladies do is listen to these lying cheating men. What makes us think they even begin to know what is going to happen . They can say whatever they want but it isn't going to make it so. Get your legal advise for legal through the military then maybe if you can get a private attorney to represent you. We certainly feel your pain and are in your corner.
My husband is military and I talked with my lawyer and YES you can get support taken from his checks and sent to you. He wont even see the money. A perk to being married to someone is a government employee. I so bady wish the divorce was over. Its going to start getting ungly here real fast in the next month.