The mother's marriage to another man does not automatically relieve the father of his duty to financially support his child.
The father will have to continue with whatever child support he has been ordered to pay. If there is a qualifying change in the mother's financial resources (perhaps due to the income of the new husband), the father may be able to ask the court to review the child support amount.
If the new husband adopts the child, the father would be relieved of his duty to pay child support.
The father should review his facts with an attorney.
The question is: What does the mother's getting married have to do with the independent obligation your bf has to support his child? The court sees these as two different things--unless, as Mr. Nguyen states, the new husband wants to adopt the child (which would involve your bf ceding his parental rights). Short of that, your bf is still on the hook for support.