Generally when confronted he will either deny doing it, claim I was exaggerating it or give some kind of explanation as to why what I said/did was deserving of such a response. He REALLY cannot take any criticism
This is entirely unacceptable. Presumably his stress anger is reserved for you, he doesn't get this way with anyone else? So he sees your role as "whipping boy" as it were...he's stressed, you pay the price. How long is he going to be in this job - years? Does this mean years of putting up with unacceptable behaviour?
Your home is supposed to be your haven. Not a place where its "right Ive had a long shit day, so Im going to put my key in the door and pick arguments with my partner".
He is a grown man. If he wanted to get help to address his out of control stress levels and subsequent behaviour towards you, then he would. He is out of order. He can't take criticism but you have to put up with this shit? How disrespectful. What gives him the right to treat you or anybody like that. Being stressed at work is NO excuse for this sort of thing
Give him an ultimatum. Tell him categorically how you feel. Broken record technique, if he won't listen.. Don't let the conversation divert, don't rise to any bait, and don't make it a long talk either.
He either gets help via seeing a therapist , or he gets out. No in between.
Don't make the mistake of becoming his pseudo-therapist either, and don't go to counselling with him if it comes to that. You will simply sit in session whilst he tries to deflect his issues onto you. Do go on your own if you feel the need to
Don't put up with it for a day longer