I'm sorry, but I don't understand your response. I think you're saying that it is NOT possible for the class quests, but it is for the others. It seems that no matter what the quest is, when either of us goes through the green door, we become invisible to each other.

When I'm playing with a friend (we're both the same class) and we enter a green door instance, my friend becomes invisible even though I can still see him on my mini-map. Is there a way to enter the instance that we can play it together?