When a man divorces a spouse who makes more money than he does, who has to pay the child support? Does the house have to be sold when there are children involved? When a woman makes more money than the spouse, does the man have any obligations at all for her and his children?
Child support is often based upon the custody arrangement. If the wife has more custody time and therefore pays for more of the care of the children she would receive support, even if she makes more money. If the custody arrangement is equal, in your scenario the father should receive child support or there would be no child support paid. I cannot answer your question specifically to the laws of NJ as I am not licensed in that State. However, I do not know of any jurisdiction that requires that property be sold, regardless if there are children of the marriage. The fact that the parties have children often makes it less likely that house will be sold. If the wife makes more money than her husband, he would not be required to pay maintenance (alimony) and in fact maybe entitled to receive maintenance from the wife. He would still have an obligation to help support his children.