Very bluntly, you've already lost your husband, and the marriage you had (or thought you had) is over. To be honest, I don't really think that the BS's response in any way promotes or discourages reconciliation; "pushing" him to go NC will not change his decision. He's made it already---he just hasn't been strong and/or honest enough to communicate to what he chooses to commit.
For YOUR emotional health (because yes, yours is every bit as important as his), it's critical that he commits, one way or the other.
Having strong boundaries and enforcing them will promote YOUR emotional well-being. It may or may not have an effect on your husband. One thing you'll learn pretty quickly is that you can't control your husband's thoughts, feelings, or actions--even though right now, you feel as though your responses will do just that. They won't.
Choosing actions that are empowering for YOU will not change the course of your marriage; only your husband's commitment to your marriage will do that. However, choosing actions that empower you will profoundly affect your self-esteem at this esteem-crushing time.
What remains to be determined is whether he is willing and/or able to do what it takes to build a NEW marriage with you--one in which infidelity is NOT an option as a "coping" technique.
Going NC is the bare-bones necessity for demonstrating this willingness/commitment.
I do understand that he is mentally ill. But PTSD does not remove his ability to distinguish right from wrong.
It does not excuse an affair.
It does not preclude absolute NC with a woman willing to destroy him, his marriage, and his family.
While you can (and undoubtedly will) empathize with his struggle, it's imperative that you not accept it as a reason for his infidelity.
He wasn't too emotionally fragile to lead a double life in which he knowingly harmed you. Therefore, he's not too fragile to man up and establish firm NC.
Millions of hugs to you. I know it's difficult; my husband was both physically and mentally ill when I made the decision to separate. Those illnesses were egregiously exploited, by him, to keep me in the marriage, accepting the utterly unacceptable. I ended up not only crushed by his infidelity, but also struggling with massive anger at myself. I hated myself for tolerating the neglect and abuse and manipulation for so long. And that anger has been far more difficult to recover from than anything my husband did to me or our marriage.
Don't lose yourself in this. Establish boundaries and stick with them. You will be glad you did, no matter what the outcome, marriage-wise.