I have to disagree with the writers above about finding a lover of your own. It sounds like that is not what you want, and if that's true it won't help a thing. If I understand correctly, the problem is not only of you not getting enough sex but of not getting enough sex from your partner.
Also, I think the cheating&lying-finding out-"giving permission" -pattern you have going on is way more troubling.
It really doesn't sound like your husband respects you very much. He lies to you and treats you not like a equal partner but like a mother or basically somebody who is out to spoil his fun. You write that other than these problems he is very good partner for you. Does this mean that the disrespect for you only exists in this area of your lives? If this is so, then the best thing to do would propably be for you both (especially him! but he must be willing to do the work) to explore why this pattern of behaviour continues. And if it is something he might be willing to change (thus far doesn't seem like it).