I'm so sorry you have found yourself in this situation. I think if it were me, I'd be talking to my therapist and to my lawyer. Your husband's accepted that he's going to settle for living a lie, but that forces you into living a lie, also. I am sure he loves you and the kids because you are his family, but now you know how he really feels; he wishes he'd never gotten married, and it sounds like he's considered transitioning. He's not the person you thought he was, and your marriage isn't the relationship you thought it was. Now you have to decide if you can stay married to him, knowing all this. You need to think about what you want/need out of life. Can you get what you want emotionally by staying married? What about financially? I have several friends who've been in "situations" but chose to stay married because of their ages and retirement issues, of not wanting to try starting over, not wanting to grow old alone. Can you rearrange your life so you are able to stay married but live sort-of independently, more as roommates than as spouses? These are all things I'd be considering, if it were me, and while I might choose to stay married, there would be big changes in our living situation, the things I do for him, and of course I'd be talking to a lawyer, just to make sure that my finances were secure.
I'm sorry- I know how much this hurts. I watched my sister go through a divorce, after being married for almost 20 years, because her husband finally told her the truth and came out. When reading your post about how you are feeling, my stomach was churning, remembering the shock she went through. Please keep going to your therapist; you've never needed the support that you need now. It might not be easy, but you'll get through it; just make sure to keep it on your terms, so that you get to choose how you want your life to be now.