Your H sounds exactly like mine did the first go around. DO NOT TRUST HIM! I cannot say that enough. Please act like he has been abducted by aliens and he is just a stranger in your H's body. He may come back, he may not. But please if I can help you with anything it is to believe nothing that he says. You must protect yourself financially and protect your children because right now you nor the children are a priority to him.
Your situation is so new, please try your best to not contact your H unless it is an emergency and only respond to him if it is regarding kids or finances. He wants to get attention from his OW let him... let him miss you. Let him see you happy and going on with your life. Fake it as much as you have to, eventually you won't have to fake it. DO not tell him you miss him, let him think you are moving on. I know it sounds like a game but trust me begging, pleading, letting him knwo you miss him will not work.