If you're in a relationship with a significant other that will not let you make him feel better, there is a chance that he could be very dangerous to you..no matter how many times he says "I Love You."
Men should not get mad or moody over little things. Those are the traits of someone who cannot take care of themselves, and most likely will result in worse consequences if he does not learn to control his emotions.
You may not agree or see any danger, but if you really do care for him and would like to take steps to solve your question, you might first think back to who his last girlfriends were (if you knew any or could get in contact with them, and discuss with them the problem.
Most past gf's of anyone know more about his actions than asking his friends. It would be a good idea to tell your friends how he's acting around you, and strengthen your connections.
You could try reasoning with him.
Ask something like "Why would you act angry over "______" like this infront of your girlfriend?
If he can't reason with his actions in both of your favors, then he's not someone worth your effort.
I really hope you get this figured out! I'll be waiting to hear how it goes.