Gosh, it looks like I might be a lone voice on this one but I think from what you have said about how you feel, that you should ignore the overwhelming body of advice in this thread for the moment. You have clearly had a huge shock, your husband is treating you appallingly and behaved dreadfully. BUT your initial instinct is to save your marriage and I think you would deeply regret rushing headlong into what other posters have suggested if you feel this way.
While unlikely, there is indeed a chance that what you have been told about the level of his involvement with this woman is indeed true. It may be that your husband is as daft as all that, to risk your entire marriage on a crazy whim. So, if it makes any difference to you, you are quite entitled to judge that what he is telling you is the truth. That may make a difference in how you want to proceed, or it may not. But I don't think people on the internet can automatically guarantee that he is lying hugely to you - it is up to you to judge.
Now, this is my terribly old fashioned viewpoint but I do think that things like this crazy notion of his are covered by the "for better, for worse" part of the marriage vows. Yes, it is dreadful, dreadful that he has hurt you in this way and completely utterly disrespected and disregarded his vows to you but you are quite entitled as his wife to want to explore how you can overcome this and save your marriage IF THAT IS WHAT YOU WANT. Even if he is willing, it will take masses of work for you to forgive him and rebuild trust, but to my mind, it is worth stating your case very clearly and making it clear that your aim is to keep your marriage, if that is the case. I do not see this as "begging him to choose you", I see it as one adult partner in the relationship remaining true to his/her current wishes and the original vows and stating your case. A tit-for-tat "well I don't want you either" reaction purely for the sake of it is childish if that is not your genuine feeling. From what you have said, I think you will regret not even trying this. Now of course it of course possible, even likely, that he says he doesn't want to try, or that you decide along that journey that it is too much for you to overcome but at least you gave expression to your feelings and tried to stay ture to them. Woukd he go with you to, say, one marriage guidance session so you can express all this with support?
Having said all that, I completely agree with taking practical steps to ensuring that he cannot take reckless actoons that woukd impact your financial security etc so it is prudent to look out for yourself and seek legal advice on thise aread. But you know yoyr own relationship, you know your own feelings, it is very eady for strangers on the internet to say "toss him out on his ear and never give him another moment's thought" but please know that it is perfectly alright too to want to save your marriage and to be prepared to work to overcome this massive hurdle. So if that is what you want, I think it is the more difficult and braver action to try to pursue it.
I will probably get slated for this, but what the heck...
Best wishes.