I’m sharing my journey not as a "how-to," but as a perspective you might want to discuss with your partner. Personally, I found separation to be the absolute key to my healing.
I separated fairly immediately upon discovery. For about a month, I was just a total mess—drinking too much and barely surviving. I took time off work, which, at the time, I couldn't really afford to do. But I was drowning.
After that mourning period, I heavily attacked dating. I can tell you honestly: this was the single biggest factor in my early survival. Meeting others was the only way I found I could fix my shattered self-esteem and my sense of masculinity. Now, in hindsight, I’m not sure it was the "healthiest" solution, but when you are drowning, you don’t care about the quality of the raft. It didn't take long to learn I had plenty to offer others; I wasn't resigned to being single for life.
However, I probably spent to long in that that phase and eventually hit a wall. I dated heavily for 4 or 5 months before the diminishing returns set in. The first few people made me feel a hell of a lot better, but by the end, I realized it was barely numbing the pain anymore.
That was my turning point. Only then did I finally look inward. I discovered mindfulness, self-help work, and jumped head-first into physical hobbies like boxing and running.
I’ll be blunt: I cannot imagine healing while in the proximity of the person who caused the pain. For me, the "tiredness" your husband is feeling comes from the fact that you are the trigger.
A few things to consider from my experience:
The Impasse: You feel like you are "managing" the ordeal, but the processing is missing. In my experience, you can't process the fire while you're still standing in the smoke.
Life Factors: I was in my late 20s with no kids. We owned property together, which was a total nightmare to untangle, but outside of that, we had no shared obligations. That made the split easier than it is for some, but the emotional necessity was the same regardless of the paperwork.
Perhaps my journey won't be applicable to your specific life, but I’d put a strong case forward for separation. He wants to "feel normal" again, and for many of us, "normal" is impossible to find when we are constantly reminded of the trauma just by looking across the dinner table.