What are you and your husband holding on to exactly? I do not mean to be harsh, but it sounds like the marriage is as good as done. Do you two happen to have children and they are the reason you two are trying to stay together? If my DH came to me and said, "Hey. My new girlfriend wants me to be mono with her, and I am not sure where that leaves you or even us," we would have nothing to talk about. Divorce would be the only option. I am no one's option or point of settling. The new girlfriend is a cowgirl as Idealist pointed out. I am usually not an advocate for ending relationships prematurely, but it sounds like the marriage has ran its course as you have moved out of the bedroom and have another relationship.
Could your source of anxiety be stemming from the fact that your role in his life is not quite as clear as it once was? Could it be stemming from the uncertainty of your future? Anxiety has many different sources and triggers. I am not sure how you can narrow it down. Do you have any idea why he is or has been depressed? Is he seeking help for that? Is it possible for you and your husband to work on being friends and learning to communicate with one another without expectations?