I know it's hard. I have had to call the police on my H too. He did not physically touch me, but he threatened to kill me.
Your H chose to deal with his depression by getting drunk. He got drunk and was not thinking rationally and took his inner anger out on you. This was not right, drunk or not.
He needs help and you are not the one who can help him. You need to give him his space. In a few days he will calm down a bit and will contact you.
I just want to also warn you to watch your guard. He may be angry that you called the police on you and may try to retaliate.
That is what my H did. He was here one night and started a verbal argument with me and then when I asked him to leave he called the police on me. The police did not understand why they were called. H had no reason to call them, just that he wanted to get revenge.
I understand about not pressing charges, as I did not press them either. The police told me if I did then I would have to get an order of protection and exchange the children with him at the police station. I did not want to expose them to that.
However, my sitch was a tiny bit different than yours as he never actually touched me.
In my opinion, if he ever does lay hands on you again, you may want to consider pressing charges. He needs to know you won't tolerate it.
I know in my state, if my H threatened to kill me again, the police would arrest him as the first time is only a warning and the second time they would press charges on him whether I wanted to or not.
I am sorry you have to go through this. You need to find a way to just focus on you and your daughter now. You need to leave him alone to spin in his own mess. He is not the person you would want to have as a husband right now. You need to realize you deserve better and he can't give you any better right now.