Marriage counselling is a completely different way of working, if you have someone there for support they should have no part in the session and if she thought you needed marriage counselling that's a discussion for her to have with you. It sounds like you were in the "marriage" session before you knew it and hadn't given informed consent.
So no, it's not normal but honestly, neither is having your husband sit in in your sessions.
Does he need to be actually in the session? Would it be enough to know that he's outside if you need him, your session is your confidential space - what happens if he brings up something at home that you've mentioned in session? He can't unknow what he knows and it will influence your marriage for him to know the content of your therapy sessions. All of that should have been fully talked through with the therapist before she agreed to him being present.
I also wonder how you can speak freely about your relationship with him sitting there - I know it would be utterly unreasonable of me to talk about my marriage with my husband present and expect him not to respond or engage in that conversation. And while my therapy is focussed on me and my trauma, my marriage does fall for discussion within the session.
In your shoes I'd need to acknowledge that boundaries were at best a bit blurred within the therapy and both find a new therapist and not have my husband come into my session with me.
