Yes, you can reconcile! My H, who I adore, had a 6-year-long A that I found out about less than 6 months ago and we have made tremendous progress.
Besides the remorse and the NC and the IC, H has shown me through his actions that he has zero feelings for her and that he wants to spend the rest of his life making up for what he did. So far, he has done a stellar job.
Your H ended this A over 2 years ago and is with you! It should be pretty clear - I hope - where his heart is. Talk with your H. Tell him how much you are hurting and let him help you to heal.
BTW, I am sorry about your having gone through cancer. I look at the timing and see we have something in common. It sounds like your FWH started his A shortly after your diagnosis. Mine did too. He says that "part" of the reason for the A was fear that he would lose me...I pray you are cancer-free now! Please take care of yourself. You have been through a lot.