That's true and in that case, he's still a player or a gyallis. Coz a married man who has girlfriends he is hiding from his wife isn't an archetype family man who is supposed to be loyal and not break his vows.
No, the man you described is not a perfect example of a family man. Marriage is supposed to be about loyalty and fidelity. If one partner strays, the other partner has been betrayed, which breaks up the relationship's trust. It's not fair for a husband to have multiple partners and expect their spouse to remain faithful and loyal to them in return, it goes both ways. If there is no honesty or fidelity between married people, then they cannot build or maintain a strong relationship together as a family.