All comments below are obviously just my personal opinion. I do not know you, your husband or any specific details of the situation. I freely acknowledge that I have employed some very broad, sweeping generalities in my characterization of men and I admit that there are many, many men who do not fall into these general guidelines.
Colorado,
If I had spent the last 10.5 years dealing with a partner who was reluctant, at best, with respect to sex I can assure you that my libido would be long dead.
Even the archetypal, super libidinous, ready at a moment's notice male will eventually realize that his partner is just not interested and be forced to make a choice between 1) finding another relationship which is sexually fulfilling or 2) accepting that his sex life is dead. One would hope that if your DH decided to go with option 1 he would end the marriage first which brings us to what I consider the much more likely, and difficult, situation; he has learned to sublimate and ignore his sex drive.
A man's sense of self-worth and his sense of validity as a MAN are very often inextricably linked to his ability to please/take care of his partner. After receiving nothing but rejection for this long it would be necessary for him to completely ignore any desire he has for you so he can maintain any degree of self-esteem. In his eyes, you are in no way physically attracted to him and any intimation otherwise is to be met with extreme cynicism and doubt. After all, you haven't really wanted sex with him in so long, why should he believe you do now? Most likely he believes you simply want to have sex with someone, anyone, and he happens to be the most convenient body.
In order to reverse his tendency to ignore his sexual feelings you will need to prove to him that you really desire HIM. Think of all the (non-sleazy and some of the sleazy

) things men have done in the past to attempt to get you into bed, these are exactly the type of little declarations you will need to make to convince him you are really interested in him and not just sex. In other words, you are now the pursuer and you need to convince him that he is the sexiest, most desirable person on the planet.
Welcome to our world.
~LTL