If you don't already have a family court support order, get one now. According to Louisa Floyd, Senior Attorney at DC 37 Legal Services, the father's child support obligations will continue while he is out of the country. If he doesn't pay, they'll accumulate. You could sue him for arrears if he returns. Ms. Floyd said also that if he's got assets here such as a house or bank account, you could get a lien against them.
Some countries have reciprocal agreements with the United States to enforce child support orders.
You might be able to enforce a U.S. court order against your husband in a foreign country. Q. I came here legally with my two children on August 21, 1992. Their father had been here since 1991. He left Hungary after I divorced him in 1986. He won the green card lottery, so he and our children became permanent residents.