Most Helpful Guy
Believe him, leave your heart open to life, and get a lawyer.
He's not earned your trust if he repeats the mistake of cheating. Open relationships are one thing, monogamy is another. He obviously thinks it's okay for him to run around when you don't. So believe that he doesn't respect you and you deserve better.
At the same time, don't condemn all men. We're not all like him. It will hurt, betrayal always does. And as we get older, it's easier to let our hearts and minds develop concrete patterns. So do yourself the favor of pushing that heart of yours towards moving on. Join OKCupid or eHarmony and make sure you talk to some other men. Make sure your husband understands you're separated, and make it a legal separation before you date. If he can make it look like you're cheating too, then it's a no fault divorce.
Get a lawyer, get a lawyer, get a lawyer. My divorce was amicable and we didn't use them. But after 24 years, your man has probably developed a cold war attitude and will lie to you about his pension. His other woman may want it, too. So lawyer up. And make him pay the legal and court costs while you're at it. Don't be vindictive but at the same time protect yourself from an obviously dishonest man.