The short answer is no. You can sue him for a legal separation and use the adultery as a basis for the separation. Or, if you have a claim for alimony, you can use the adultery as a factor to get alimony. NC statutes provide that if you are a dependent spouse and he is a supporting spouse that has the ability to pay, if he committed adultery it is presumed that he shall pay alimony. There is, however, no cause of action for just "adultery." You can sue the girlfriend for alienation of affection and criminal conversation for breaking up the marriage and sleeping with your spouse though.
You can use this allegation against him in a claim for adultery if you first demonstrate that your husband was the financially supporting spouse in your marriage and you were financially dependent upon him. You also may have claims against the woman for alienation of affections, criminal conversation and related tort claims.
This answer does not establish an attorney-client relationship and should not be intended as a substitute for legal advice.