Hi,
My first X came out as gay 5 yrs into our marriage and we stayed married for 8 more. The kids were born when I was 17 and 19 so I had no higher education or real job skills. He wasn't a fantastic Dad, he was more into work than the kids but he provided and at that point that was necessary. He went out and did his thing and I had someone I saw twice a month, a friends with benefits thing.  In the end it was a few things that finally had me asking him to move out. 1. He became a solid alcoholic. He drank whenever he was home and when he wasn't, he was out at a club trying to find a guy. 2. Dut to 1, he lost his license after his third DUI and we lost our insurance because he kept totaling cars. I had to find a way to go to work more hours and was having to depend on relatives I did not want to depend on to watch the kids. 3. I caught him in the living room of our 650 sq ft apartment having sex with a male partner while the kids and I were asleep in the bedrooms. It could have been the kids. That wrapped it.  
I believe the drinking started because he had self hate for being gay (he was raised strict Catholic). 
If you and your husband can have separate bedrooms, or better yet, floors in your home (basement bedroom kind of thing) then I'd say if you can get along otherwise, and if you can each have your needs met in a discreet way then, sure, it's possible. At least for a while. But if you try to just keep fighting to keep the marriage the same, I'd say it's not going to work. Kids feel that mess. If you can afford to raise them on your own in a safe area, I'd say prepare for that to happen. If you need to get some skills before then, this is your time to do that. Please believe me, you'll be happy to make as much money as possible. (heck for all I know you make good money. Just sayin') Anyway, once we did divorce, I was happier except for money. Brings to mind that saying "You'll know you made the right decision when you feel peace in your soul". But sometimes that peace requires some planning. I'd sadly expect the marriage to end sooner or later, and start planning. Wishing you peace. Oh, yes we did ok coparenting afterward because he just saw them for 2 hrs every other week and I did....everything. But the man paid every penny of child support, and bought them school clothes, etc. So I don't diss him. The kids are now in their 40s. Their kids once called him their Uncle at a Christmas party, so that says something.

Figuring it out,

I'll give you my perspective..biased as it is.  I don't have experience co parenting really young kids.

My kids were teens when my GX decided she wanted to have a gay affair. There seems to be something, and I've seen here, that when the kids become teens these spouses want to do their bad stuff...like they see the teenagers having fun and they want to be teens again.   The problem with this is it's usually not with us.

I would say you could stay with him and save money and raise the kids. But I'd be wary as yourselves and kids get older.   In sentence after the kids are gone and moved out are you the one he wants to spend his later years with?    I'll always cherish the years I had with my kids and her when they were younger..we were good parents.  But it's a scary thing to think that I was never in her plans. And that she had no loyalty ..and she showed the kids that it was ok to treat me like crap.

Whether you stay or go the kids will always have a mom and a dad.  Question is whether you can live with your spouse knowing that his loyalty could change.