Welcome to the greatest bunch of folks that you never wanted to meet. I'm sorry that you're here.
You've started well: You haven't decided whether to R(econcile) or D(ivorce) yet. You know that IC for both of you is required before you can begin MC. Honestly, he'll need more than 4 to 6 visits to his IC to work back to what allowed him to think that having an A was a good answer to any question that could be asked. This can take a while.
It also sounds like you know that, before a MC can be effective, that both parties entering into the counseling have to be all-in on being truthful and open with the MC. That's just like going to the doctor and complaining that you have a sore throat when you want the doc to fix your broken leg. If you leave with your leg still broken, well, you can't expect the doc to be a mind reader. You have to tell professionals what the problem is, fully, openly, and truthfully, before you can expect them to be able to help.
If you read in The Healing Library (yellow box, upper left) you can find the BS FAQ. Item 11, The 180, is a tool to help you distance yourself from the problem a bit to allow you to think more objectively about the problem and how your W(andering)H(usband) is acting. Cheaters lie to cheat and they keep lying to "avoid hurting you" when they're really lying to make things easier on themselves. Cheating is a wholly selfish way of thinking. You have to get used to the idea that your WH can be wholly selfish, which might be foreign to you. Also in The Healing Library are a lot of links to online Articles and Book titles that are good. You should read in The Healing Library a lot. Knowledge is power.
Another thing to remember is that the choice to have an A is 100% the choice of the cheater. You did not do anything that "pushed" him into the A. He had other choices, like 1) walking out and filing for D, 2) demanding counseling for the two of you, 3) talking to you about any problems.
And an A is not a mistake. It took a long series of _choices_ to have an A. Each step was a choice. A mistake is forgetting the milk when you go to the store. An A is not a single mistake.
Your H's sibling is already protecting herself over her H by not telling him. Don't let that attitude rub-off onto your H. And, if you do decide to R, then going No Contact with that sibling (and perhaps that whole side of the family) is going to be a requirement. You cannot heal while that sibling is still around. IMHO, anyway.
You might think about keeping your posts in this thread for a while. If you do then new readers can read your first post and get your story and then jump to the last page to get your current status. Not a requirement, by any means, but it helps people helping you.
Also, when reading on SI "take what you need and leave the rest." Some other posters are still very raw and you might read a few posts exhorting you to "D, now!" or that seem particularly angry or demanding. Do not take it personally. Mostly that is like a person watching a horror movie and shouting at the screen, "Not in the attic! Call the police, now!" or similar.
Lastly,
Drink - water or juice, and no alcohol for a while. You need to stay hydrated and alcohol is a depressant.
Eat - food of some kind, even if it is protein bars and vegetable or fruit snacks throughout the day. You need to keep your strength up and your electrolytes in balance so that you can think properly. Ensure, Muscle Milk, smoothies, and Gatorade are your friends if you can't seem to keep food down.
Sleep - as much as possible. Melatonin is an over-the-counter sleep aid that helps you to be drowsy but doesn't knock your ass flat out.
Doctor - if you are having particular troubles with drink, eat, sleep advice a doctor can help. You also need to be screened for with a full-screen STD set of tests. Advise them of the A and tell them that you want to be tested for everything. Chlamydia, trichomonas (sp?), Hep A, B, and C. HPV. HIV. Herpes Simplex Virus (HSV) 1 and 2, gonorrhea, syphilis, and anything else that they can think of. Your H needs to be tested, too, and you might think about going with him to make sure that he doesn't lie about why he needs to be tested.
Honestly, you're doing well at reacting to this. Learn, read, and remember knowledge is power. Carefully think about seeing a Lawyer to at least know your rights in your State.
Lastly, check with your and his workplaces to see if either of you have an EAP (Employee Assistance Program). Many workplaces do and you can get some free IC / MC visits and/or recommendations for a Lawyer from the EAP. They're handled by an outside firm and don't report specifics back to your workplace. Naturally, any doctors that you see will at least show up on your workplace insurance, most likely.