I am in full agreement with NOPkins on this, there is no way you are going to get your M back on track while someone else is in the picture. You need to decide what you want.
And you do need to confess to your H, a strong M is built on trust....you have compromised that trust. I'm not saying that to be mean or anything like that...it's the simple truth. Right now you are living a lie...and you are forcing your H to live a lie....and that's not right....to either of you.
This same advice has been given to others on this board who have come here looking for advice....who have also cheated. To begin rebuilding your M you MUST start with a clean slate and give your spouse the knowledge to make their own choices and decisions as well.
Unfortunately what you are doing now, intended or not, does have consequences. You owe your H the truth....you do not have the right to take away his choice of staying w/you or not by witholding the truth from him....and thereby forcing him to live a lie unknowingly.
I know it's a VERY difficult thing to do, coming clean with your H, but if YOU want to have a chance at rebuilding your M...it's absolutely necessary. Look at it this way....it's not going to hurt him any less right now...than it will weeks, months, years from now when he finds out (and eventually it will come out, things like this always do.)
Go to him, tell him what's happened.....but tell him you choose him, and want to fix your M and you are willing to do anything to do that (if that is in fact the avenue you want to take.) But you must end all contact with the OM immediately, I cannot stress that enough.
You have come to the right place for support and we will be very honest with you as to how we situation, so be prepared for that....but I will repeat myself, you must stop your "A" if you hope to repair your M.
Also, please start your own thread so that we can keep up with you without hijacking this particular thread
FYI, I too am a SSW, married to an LDH....so please understand I do know where you are coming from. I have been tempted, I have had offers, I simply chose not to take them.