I've been in this industry for twenty years and, while it took my wife a little while to get used to my schedule (not long), it's a normal part of her life now. She's never had a reason to worry about me cheating on her either. Also, your husband can easily stay in shape in this industry, as long as he's committed to it. I always try to find a gym within hotel shuttle van distance at my layover cities, and I make an effort to actually eat well all the time. It can be done.
It'll be a little different for you at first, but you'll get used to the schedules. Whenever possible, you guys should take advantage of the travel benefits and go somewhere. It's a heck of a perk.