You can't be forced to take custody. Your husband can sign away his parental rights and surrender the children to foster care. You should be prepared to make payments to the state for the care of his children. I'm not sure if they do this, but I suspect they would. Here is the NJ code pertaining to your situation.
9:2-14. Surrender of child custody; validity
Except as otherwise provided by law or by order or judgment of a court of competent jurisdiction or by testamentary disposition, no surrender of the custody of a child shall be valid in this State unless made to an approved agency pursuant to the provisions of this act or pursuant to the provisions of a substantially similar law of another State or territory of the United States or of the Dominion of Canada or of one of its provinces.
L.1955, c. 232, p. 896, s. 2.
9:2-15. Surrender or termination of rights of one parent; rights of other parent
No surrender of custody by, nor termination of the parental rights of, one parent shall affect the rights of the other parent; nor may one parent act as the agent or representative of the other parent in the surrender of custody or termination of parental rights.
L.1955, c. 232, p. 896, s. 3.
9:2-16. Voluntary surrender to approved agency
An approved agency may take a voluntary surrender of custody of a child from the parent of such child, or from such other person or persons who, by order of a court of competent jurisdiction, have been substituted for the parent as to custody of such child. Each such surrender, when properly acknowledged in the manner and form provided by sections 46:14-6 and 46:14-7 of the Revised Statutes, shall be valid whether or not the person giving the same is a minor, and shall be irrevocable except at the discretion of the approved agency taking such surrender or upon order or judgment of a court of competent jurisdiction, setting aside such surrender upon proof of fraud, duress or misrepresentation.
L.1955, c. 232, p. 896, s. 4.
9:2-17. Form of surrender
The form of any such surrender shall be such as to declare that the person executing the same desires to relinquish the custody of the child, acknowledge the termination of parental rights as to such custody in favor of the approved agency, and acknowledge full understanding of the effect of such surrender as provided by this act. Any such surrender may include a statement that its purpose is to permit the approved agency to place the child for adoption by such person or persons as the approved agency may select.
L.1955, c. 232, p. 896, s. 5.
9:2-18. Procedure to terminate parental rights
6. An approved agency which is providing supervision of a child may institute an action in the Superior Court, seeking the termination of the rights of the parents of such child and the transfer of custody of such child to the agency. A prior surrender of custody as provided by Article II of this act shall not be deemed a waiver of notice or service of process in proceedings under Article III hereof. At least five days prior to the hearing, the plaintiff shall file with the court a written report as to all circumstances of the case.
L.1955,c.232,s.6; amended 1991,c.91,s.192.
9:2-19. Grounds for terminating custody
If the court shall determine that custody of the child has been surrendered as provided in Article II of this act, the court may declare that the person making such surrender shall have no further right to custody of the child. If the court shall determine that a parent of the child is dead, or mentally incompetent, or has forsaken parental obligation, the court may declare that such parent shall have no further right to custody of the child. If the court shall determine that a custodian or guardian has been appointed for the child, but that such custodian or guardian has willfully and continuously neglected or failed to discharge the responsibilities of such appointment, the court may declare that such custodian or guardian shall have no further control and authority over the person of the child.
L.1955,c.232,s.7; amended 1990,c.26,s.4.
9:2-20. Judgment terminating rights; effect of judgment
If the court shall find that the parents of the child should have no further right to custody of the child, or that the custodian or guardian, if any, should have no further control and authority over the person of the child, a judgment shall be entered terminating such right or control and authority and transferring the custody of the child to the plaintiff. The judgment so entered, unless otherwise specified therein, shall not affect the duties of the parents, custodian or guardian with respect to support and maintenance of the child.
L.1955, c. 232, p. 898, s. 8.