I've known a few. It takes a special couple. If there are trust issues they must be resolved. Not impossible.

First off, are you saying celibate, or monogamous?  One means that he's having sex with no one - even with you.  The other means that he'd only be having sex with you.

The other thing is that if he were capable of doing either of the above, wouldn't he have already done that?  If he's already cheated and lied, what makes you (or him) think that he's more capable now that he's already failed at that?

Kel

There's a yahoo group for Monogamous Mixed Orientation couples but I couldn't find it.  The name is abbreviated (something like monMMOMW), which makes the search difficult.  I did find the non-monogamous group:
https://groups.yahoo.com/neo/groups/MMOMW/info?yguid=300400474
You can ask there for the monogamous group and whether it's still active.

In addition to the key issue of trust, there are some other big challenges you face.

First, suppressing one's sexuality is sort of like holding an inflated ball under water indefinitely.  It requires constant effort to keep the ball submerged, and all the energy expended doing so takes a heavy toll.  Very frequently, closeted men fall into a "walking" depression where they function but they live a joyless life.  This negatively affects all their relationships, but most especially the one with their wife.  For her it's like being married to a wet blanket, only worse: there's an emptiness that can easily engulf both of you.  When it does, it happens subtly.  It's not until you experience genuine joy that you realize how numb and empty you've become.

Second, having children together is often the fundamental reason mixed orientation couples want to stay married.  Both parents enjoy family life and they don't want their children to come from a broken home - not to mention all the disappointment and heartbreak that splitting up would create.  Eventually, of course, the children grow up and they're no longer the marital buffer they once were.  Before too long the marriage is at serious risk of collapsing.  This means that staying together in your 30s or 40s often means divorcing in your late 50s or early 60s - not great ages to be single and meet someone new.  And of course, the divorce that you desperately wanted to avoid happens anyway.

Finally, being married to a gay man means being married to a man who has no genuine desire to be with you as a woman.  Yes, you can be the very best of friends, but that's not the same.  The lack of authentic desire tends to play out in multiple, subtle ways.  The biggest is that the woman's self-esteem is non-existent.  Another is that the couple is not a good role model for their children, especially daughters.  It teaches them that women are not to be valued - that *they* are not to be valued.

Logically, it makes perfect sense for a mixed orientation couple to stay together if the man commits to being monogamous.  But the reality is much more complicated.  In my opinion, from the wife's perspective, you sacrifice nearly all of the joy of life, and ultimately you get very little to show for it.  A good marriage and being a good parent DO require sacrifice but in both cases there are tipping points where too much sacrifice does more long-term harm than good.  A mixed orientation marriage, even a monogamous one, can easily fit that description.

JKPeace
I'm pretty much in your place now.  My husband of 30 something years was found out although he still denies everything.  We have one daughter who is 15, and husband knows i want a divorce, but he can't handle it and is using my daughter as the reason to stay together.  He's proposing all kinds of fantastical plans, but I think the bottom line is he does not want to come out to our daughter or his family.  he wants to stay in our house for 3 years until daughter goes off to college.... and then what,.... we divorce and she is off with no support system...does not sound like a good plan to me.  I feel strongly that the role models she is getting at home, are not ones I want her to have for future relationships, and her own self worth. Two happier homes is better than one messed up one right?