It doesn't have to be to the point of you feeling in danger though. It sounds like you're saying "oh he's just shouting and I don't think he's going to hit me so it's ok."
Anxiety and depression aren't an excuse to act like an arsehole. If he's fine with everyone else then he can moderate his behaviour, can you see that? Why should you, the love of his life, have to put up with being shouted at? And as for shouting at the DC - just no.
I'm not saying LTB.
There is a whole range of actions you can take to change your response to try and get him to stop his negative behaviour. It's not black and white, as you know since you did post in the first place.
For me personally verbal abuse / bullying of DC would be nipped in the bud at the first instance, and if he didn't change it would be divorce. I wouldn't give him more than 2 chances. It's just not fair on the DC and so damaging.
I understand you've given him more than 2 chances. How many chances have you given him? Do you keep having the same conversations with him over and over? Tell him that! Tell him you know he's not listening to a word you say. Ask him if he's serious about making the relationship work. He needs to realise you're not just whinging, this is a serious problem and you're going to leave if he doesn't sort it.
I'm coming at this from experience with my DH who still blows up over the smallest thing, in a totally inappropriate way, frequently. I posted a few months ago under a different name in despair. The difference now is I pull him up on it every single time there is even a hint of negativity or an inappropriately angry reaction. He knows I will leave him if he ever does it to DS. I will leave him and never look back and he knows it will be his own fault. The diatribes have gotten shorter and it doesn't happen as frequently. As to whether he's capable of permanent and deep rooted change who knows. I owe it to DS to keep going. I can totally see that DH's issues stem from a totally dysfunctional and abusive childhood but guess what - I had one of those too and have done a lot of work on myself and put in a lot of effort in order to become a calmer and more positive person. I don't expect anything from my DH that I'm not able to do myself. He knows that too as I was still a mess when he met me and has helped me heal.
That was an essay, sorry.
Do you want to keep trying with this man? If so you need to really step up in terms of your boundary setting and in defending your DC. You also need to seriously think about your escape plan if it comes to that.