There is no shame expressed by the mobsters, generally, about their girlfriends, they all have them, and they love their wives and family dearly, but just need to have other sexual venues, as well as a place to stay the night when in "the doghouse" or out very late, etc.
To learn more, watch Analyze This, Goodfellas, and The Sopranos
Boss Paul Vitti: I wasn't with my wife, I was with my gumar.
Dr. Ben Sobel: Are you having marriage problems?
Boss Paul Vitti: No.
Dr. Ben Sobel: Then why do you have a girlfriend?
Boss Paul Vitti: What, are you gonna start moralizing on me?
Dr. Ben Sobel: No, I'm not, I'm just trying to understand, why do you have a girlfriend?
Boss Paul Vitti: I do things with her I can't do with my wife.
Dr. Ben Sobel: Why can't you do them with your wife?
Boss Paul Vitti: Hey, that's the mouth she kisses my kids goodnight with! What are you, crazy?