How do I deal with unfounded jealousy?

I'm on my second marriage. We've been married for six months and have known each other half our lives. My husband is wonderful, a perfect stepfather, a perfect husband. Our only major problem is my ex. We have a three year old daughter that we share custody of, so there has to be contact. My husband was around while my ex and I were married, so he knows him personally, and also should know that I wouldn't go near him in that way if my life depended on it. Ex was a cheating, lying, mentally abusive jackass. Anyhow, for some reason, my new husband has gotten very suspicious of the time I spend talking to ex about our daughter. I've told him over and over that there's nothing there. How do I convince him?