I think your reaction is normal. Everyone responds differently to affairs, and that’s ok.

I would advice you to talk to your husband. Tell him you know about it. Tell him how you feel, just like you posted here. Maybe check out information on ethical non-monogamy and polyamory. 

Perhaps, write down your own wishes/boundaries for this situation. Do you want a don’t ask, don’t tell situation; or will you be ok with knowing the details? Want to be included in the planning? (Ex. Tuesdays and Thursday’s you can go see her). How much is he allowed to spend on her? Safe sex concerns (you don’t want any accidental pregnancies etc). Write out your boundaries and demands (if you have any). Above all, make clear to him that you don’t want to break off the marriage, but want to settle into some kind of agreement that’s fair for both of you.

Perhaps seeking out a therapist that is familiar with ethical non-monogamy will be useful for you. You can find them by googling.

Again, I don’t think your reaction is unusual. Coming from a European background myself - affairs like these are not uncommon with the spouse knowing and agreeing with it. It can help with a (hopefully temporarily) situation like yours in which libidos aren’t fully lined up. Just make sure he’s just in it for the sex and if he is also having an emotional affair - how you feel about that and if that is still ok with you.

Best of luck to you both.