G.B.:
If your "other half" is your boyfriend, bin him, he's cheating on you.
If he's your husband, either fight for him if you think he's worth fighting for, or also bin him if you can't forgive him.
Either way, the greatest and most precious asset in a relationship is trust. If and when it goes, the problems set in. And when someone's other half is keeping any kind of relationship with someone of the opposite sex a secret, they're not doing it just to p!ss you off, they're doing it because they're HAVING it off!