For the record, I do understand what you mean about being private. While many people are more out, I am as well, others aren't. DH and BF are both not out to most of their lives. For reasons that range from work reasons to just not being the type to share their private lives. It does make it difficult sometimes and DH is on this forum for that very reason! So you are in a good place.
You will find if you do a lot of reading or look around that you are not the first with this problem! Not to say it's not a big deal, just that you aren't alone! People have come here saying that they started out swinging or just open and then emotions got involved. It's a very different thing when you get emotions involved, but having emotions involved does NOT mean it has to be an either or situation!
He loves you, he loves her. This wasn't what you were expecting, not what you wanted, but like life often does, it's what you now have. So here's some questions to ask yourself:
Is it possible to continue your relationship with your husband if he loves another AS WELL AS you?
Would a long distance relationship between him and her be possible without damaging your relationship with him?
What is it you two feel you can compromise on?
What is it he and she could compromise on?
Basically, this is workable! If you want to do the work. Now, maybe you don't. Maybe poly is just not what either of you want, that's fine too. Then there are other decisions to think about. However, I just want you to know that this does not HAVE TO be a situation where he needs to choose between you two. With compromise and work it's not a definite end to your marriage.
Me: Late 30s pansexual poly.
DH: My husband of 19 yrs and father of 3 teen girls.
DC: LDR of +4 year