I disagree a bit with the previous advice, actually.
You said he had a traumatic brain injury, and that he tells you he loves you but you don't say it back. If you want him to return to your marriage, why wouldn't you say something else - like "I love you too, H" or "I love you too and I wish you would work with me to make this marriage as great as it could be".
TBIs result in depression - and sometimes a loss of judgment. Sometimes the affair is just a way to self-medicate the depression, by getting the dopamine "high" of infatuation.
You don't need to be a doormat, but you might want to make sure he knows you are open to reconciliation if he will stop the affair. Also, if you could get him to go to counseling with you, the counselor might help to get H into treatment for his depression if he's not already getting it.
He's been through a horrible experience and as bad as his behavior is now, if he was a good guy before, I commend you for giving him the benefit of the doubt. Some here have seen themselves as a lighthouse, lighting up the path home.
Do you have children together? How are you living YOUR life right now?
(I feel for you, my husband was not military but he had 6 concussions in 8 years prior to our divorce. It was not the only reason for our split, but his depression and judgment were definitely affected).
