Too much too fast is a sure recipe for hurt feelings and much disaster. I'm glad your hubby wants to have an honest talk with her about giving you some space and time, that's a positive.
As for him staying overnight, remember: breathe... If you find yourself not ready for that step right now, it's okay. I think that he should understand it's a very big step and it will take some time. You need to feel secure within your relationship with him before allowing him more freedom to develop things with her.
Hell, I have been with my boyfriend for over 2 years and he and I have never had a sleepover. Not so much because our mates are opposed, it's more due to a lack of space in his house and mine and a lack of opportunity. We don't have guest bedrooms, there are kids in both houses and we each normally sleep with our respective spouses in not so big double beds...so yeah, not happening unless someone is out of town and the kids are away, lol.
Also, if/when it happens, try to do something for YOU during the evening of said sleepover. Invite a couple of friends and have a girls night out (or in, whichever). Or pamper yourself with a nice movie, candles, a bubble bath and a glass of wine. Try to enjoy having the whole bed to stretch out in and some wonderfully quiet YOU time. He'll be home before you know it.