He'd have the same rights as any unmarried father. He'd have to first prove paternity, although your husband is presumed to be the father, in the day of DNA testing no court will refuse a request for a genetic test supported by the appropriate affidavits. If he is found to be the father he would have every right to request parenting time, shared parenting or custody. Child support would also become an issue.
Determinations of the allocation of parental rights are usually based on the "best interest of the child" standard. It is somewhat unlikely that court would order a change in custody to a father who hasn't been in the child's life (even if it wasn't his fault). However, the father likely would be able to obtain parenting time with his child.
This answer is for informative purposes only and DOES NOT create an attorney client relationship. You are encouraged to consult the services of an attorney.