The threat may be real along with his depression and PTSD, but he could also be using suicide threats as a way to stay in the home. It's very possible.

This man has proven himself to be sneaky and a liar because he cheated on you, and to be disrespectful of you by continuing to sleep with other women while still living with you now.

Why are you not enraged by his behavior and treatment of you? You're focused on his depression and mental health issues, while in the meantime he is sleeping with whomever he wishes and he gets to still live in your home.

I think it would really benefit you to look at your husband with more of an objective and critical eye.