Erm, I used to do your husband's type of job. International assignments where you stay over with your team for weeks/months at a time. You do become very close, as you don't know anyone else in this place - so breakfasts, dinners, gym etc - you become best friends.
But you're always aware it's a bubble. I certainly was. My real life was when I came home, but my team got me through being away from friends and family for so long. It's not an easy life - constant pressure to socialise, network and be your best self. You cannot switch off even when back in your hotel/apartment, because it's still technically work time. Which is why you need allies out there, or you'd have a break down.
It's also why it's a well remunerated profession.
When we'd co-ordinate dinner plans, it was very common to say, "X, I need to grab a shower and then will meet you down at x time", or we would ask/give each other advice on what to buy, where to go on holiday, gym routines to follow etc. Sure, some of the relationships (not mine) developed further, but most stayed exactly as they were - friendships. If you do a job where you need to be away, you cannot avoid becoming very friendly with the people you're with. Your success depends on them.
Nothing you've said suggests this is flirting. I've said and been in those situations, and I was married, my colleagues were married, and nothing romantic was ever considered. But this requires you to know and trust your husband. I did work with men, who never ever liked being home with their wife and kids - but the wives knew this, and tolerated it because it meant they could afford a certain lifestyle. Those men absolutely cheated, but it was so obvious who they were, and they'd be like that even back home.
I would have been enraged if my partner made me take decisions on my team/colleague dynamics based on their insecurity. I'm not sure you understand how much performance ratings/bonuses are based on how well you work/get on with your team. And going to dinner or the gym together is just the norm - you can't expect him to stay alone in his room constantly? Feeling guilty about doing your job is not a nice place to be. So unless you've noticed a change in his behaviour, feel he's not being as attentive, don't make his life miserable for just making friends at work.