As Ronald Reagan used to say, "Trust -- but verify." Yes, you have to have systems in place to verify if your husband is being truthful with you, but once in place, you have to live the moment in TRUST. Your behavior is going to push him away.
DO you have any systems in place to know if he's being honest with you? If not, perhaps you need to. If you do, and he's not giving you any reasons to doubt him, then you need to back off.