Is there a name for this kind of nightmare?

I have nightmares quite often, and usually it ends up going the same way.

Basically I'll be having a nightmare and I'll "wake up" and call out to my husband, but then I realize I'm not actually awake and that I'm just dreaming that I am.

This happens over and over until I actually manage to wake myself up. I usually can't tell if I'm actually awake, or if I'm just dreaming that I'm awake like all the other times.

I eventually come to realize that I truly am awake and not in my dream still, but then I'm so scared about falling asleep because I'm terrified of being trapped in the nightmare again unable to wake up.

Is there a name for this?