I'm losing my husband because my lack of sex drive

I have no sex drive due to medical issues. I've shut down completely and closed everyone out. I've even told my husband that I wanted a divorce since that's what I thought he wanted to hear. However, it devastated me when I learned he's seeing someone else. I've since told him that I wanted to work things out but he's not sure I actually mean it. He thinks the only reason I want him back is because I'm jealous. How do I show him I'm serious?