How can one get copy of birth certificate from cheating husband and girlfriend?

If a man is cheating on his wife and has had another child by this other woman, how can I get a copy of the birth certificate if I am not an immediate family member? I think this wife has the right to know her husband is scum. She has no clue and I can't go in with no proof.

I really don't want to stay out of it because I would hope someone tells me if my husband is having an affair.