An ex-fling of mine had bad table manners - found it impossible to eat things like chops with a knife and fork. I looked at him like
the first time he just picked one up and went for it and he was all like, 'what? What's wrong? I spelt it out for him, he gave a cursory attempt at using the K&F, then have up in exasperation and went for it with his fangs teeth.
Don't get me wrong - eating things like that with fingers is fine at home or at BBQs, when you've exhausted your knife and fork, but not from the off at a restaurant. :-/
Anyway... As for suggestions. It's a tricky one, because it's not really about table manners. Or at least not just about manners. At the heart of it, it's a criticism of the way he was raised, and fundamentlly, of his parents, so it's a really delicate issue once you look at it like this.
In a way, it's impossible to really advise on the best way to tackle this, since none of us know the best way to appeal to your DH's good nature. To say things in a way which won't automatically have him go on the defensive, clam up, and then not resolve the issue. Maybe have a think about this and work out how to raise it in a way that he might be receptive.
Perhaps have a chat over dinner - or even better, not at at the table at all! - as opposed to reacting to him when he's showing bad manners. That way he might not be as defensive. Bring it up more generally - talking about things which you feel are important to distill into your DC, and why. Maybe open it out by insinuating that there are perhaps things about you which he doesn't agree with, which you'd be open to changing just so that it's not all one-sided (and I do mean table-manner level things; not fundamental personality issues!) - but beware that becoming a can of worms.
Be sure not to go on the defensive yourself.
I dunno - table manners are important to get right, because your DC go out into the world, and rightly or wrongly, are judged on them. They just are. You need to appeal to his sense of not wanting to disadvantage them. Which is tricky because he'll say he hasn't been disadvantaged by a lack of polished manners - when of course he's probably been silently judged countless times. But pointing that out is hardly going to endear him!
Well, this is a really long-winded way of providing no useful advice at all.
I feel your pain though - it would be a big deal for me.