I think I would start counselling alone anyway OP, it can't hurt to have somewhere to talk about your own feelings whether your DH decides to go or not. If you get to point where your counsellor thinks it would be useful to see him too would he be any more likely to come if the request came from the counsellor rather than you?
Me and my DH had problems after my mc's, not so much arguments with us more just completely shutting off from each other. We both handled it in totally different ways though, he seemed really cold and detached about it to me and I got angrier and angrier with him because I wanted to know our babies mattered to him too and because I felt I couldn't talk to him. I felt like he just wanted me to shut up about it and move on so I slowly closed myself off to him until we were barely speaking and both utterly miserable.
We went on like that for weeks and then it finally came to a head and it all came flooding out. He thought he would make it worse for me if he talked about how he felt, he felt like he had to tiptoe round my feelings and that I was more 'entitled' to be upset than him (because it happened to my body not his) and that his feelings didn't matter. He thought that because I cried when I talked about it that he was protecting me from being upset by shutting down conversation about it when I tried to talk to him.
Point is, we dealt with it in entirely different ways and, once I understood that, I had to accept that his way was different to mine. We agreed some compromises so that neither of us felt unsupported by the other but we still had to get through it our own way.
I'm not saying your situation is the same, what he said was pretty heartless but, if your relationship is otherwise strong, I would at least want to try to hear his side in counselling before I made any big decisions about the future.
It does sound like some space would be a good idea in the short term but I would be pushing forward with the counselling at the same time.
for you OP, mc is one of the worst things I've ever been through and I'm sorry it's happened to you too.