It's okay. I'm a crybaby too. Sometimes I get the same reaction. I will sometimes try to go for a hug when crying, and sometimes this works. But I notice that there is less of a degree of anger when crying than when fighting. I'm not saying everyone is the same, and there is no hard and fast rule against fighting back if you feel you need to.
In really emotional times it can be a good idea to excuse yourself and leave the room too, to let everything calm down. If you want to approach a touchy subject again (the one that caused the problem), speaking in an even, business-like tone rather than in an emotional tone will often be better received and can help his reaction be less emotional too. I hope this helps.