I think it's sad to throw away 11 years of happy marriage before seeking counselling over this. It may seem like a dealbreaker due to the shock right now, and it's a natural shock, but over time you may come to accept or even embrace it.
To add my own story: I'm female, always loved anal sex as a "treat" every now and again, don't find it painful at all, but extremely pleasurable. When I met my husband he'd only tried anal with a women once before and had a bad experience, but I re-introduced him to it - he was averse at first but over time he saw how much pleasure it gave me, and now enjoys doing it with me once a month.
Six years ago I came home from a night shift in the early morning, and found him masturbating in bed with one of my butt plugs whilst wearing one of my thongs. Like you, I almost threw him out and I was totally disgusted. We slept in separate houses for a month whilst we spoke about it and tried to understand each other better. We didn't have kids at the time so it would have been easier to separate if needed. My initial fear was that he was secrectly trans as my brother came out as transgender after years of happy marriage and it led to a very messy breakup with his wife.
He claimed it was out of "intrigue" as he'd seen how intense my orgasms were during anal, and he'd read online about the male P-spot (prostate) giving similar orgasms in men. This didn't explain the lingerie though and he couldn't give a reason for that, except it was "a moment of madness".
We opened up a lot during that month and it brought us closer. We agreed to explore anal play on him as long as it didn't involve dressing in lingerie, but to compromise I bought him some stylish Calvin Klein male thongs. He doesn't wear them daily or to go to work, but for lounging around the house, and he looks hot in them!
The first time I gave him a prostate massage he shot his load so hard that it hit the ceiling (sorry, graphic detail) and I was able to see how men can enjoy the same intense anal orgasms like I do. It's a massive turn on to see how much pleasure it gives him. We've now got the level of trust and intimacy that we've explored pegging, and I enjoy using a strap-on to make love to him. There's no domination/submission involved, it's all very passionate and he doesn't ask for it, but I'll surprise him with it once or twice a year (normally on holiday when we're able to relax more away from home).
He's 100% straight and if I'd thrown him out, I would have lost my amazing life partner due to my initial shock. We now have a fantastic sex life and have no secrets from each other at all.
Good luck to the two of you and I hope you can resolve your relationship <3