Blackwell...I have to ask about this " I thought we had made a non-verbal agreement to just live this way and was OK"...WHY in the world would you assume you had made a non-verbal agreement on something like this?
I'm not coming down on you about that, but seriously WHY, in a marriage, would you "think" (think=assume) that this was the case? You two had lost the intimacy in your marriage (hence the lack of sexual desire)...you two had some major issues going on in your marriage (no question there). Was it easier for you to believe there was a non-verbal agreement, because that was easier for you to deal with than dealing with the issues? I ask that because so many people choose to avoid issues...rather than addressing them, for a variety of reasons: the time it takes to address things, money for therapy, the mere fact that they really don't want to take that close of a look inside themselves. It's just EASIER to avoid doing all of that. Assuming you had a non-verbal agreement seems like avoidance to me.
Now, having said that...there is NO excuse for cheating. Cheating is a choice someone makes, everything that is done along the way that person can make the choice to say "no, I'm not doing this." They also have the choice to say "I've had it with what's going on in this marriage, I want a divorce"....before they seek anything outside of the marriage (often that will get their partners attention). Cheating, ultimately is a choice that is made by the cheater.
Now, you have your own responsibility for the state of your marriage...there's no denying that, but NO ONE can make another person cheat.