Congrats for making it as far as you have! Balancing med school with a spouse, children, and your spouse's job (which also sounds relatively inflexible) is no easy task. The short answer is it WILL be hard--and it may continue to get harder as you progress through your training. During your clinical rotations, you will definitely have days in which you have to be at the hospital by 5:00 am (or sometimes earlier) and are there until well past dark. You will have some days where you are expected to stay in-house overnight. Your schedule will change from month to month depending on your rotation. You will have a few nice electives with relatively 8-5 hours...but these will be the exception and not the norm. And during all of that, you will still be expected to study for your shelf exams, licensing exams, and other miscellaneous research and quality improvement projects and the like.
Depending on the specialty you match into, residency may be even worse with even more hours and less flexibility with your time.
I definitely witnessed many relationships suffer and ultimately perish during medical training. But the good news is I also witnessed many that survived and flourished. I had classmates with several children who even had more children during their training--and somehow made it work.
I think you and your husband just need to be VERY honest with each other about the sacrifices both of you will have to make over the next 6+ years. Try to recruit nearby family or friends as much as possible to help with the kids.I know it sounds impossible, but try to arrange for someone to watch your kids at least once a month so you two can go out as a couple and spend time with each other--outside of the pressures of kids, studying, exams, etc. And try to find others at your school--or perhaps online--who are in a similar situation. Most of your classmates are likely single or in relationships but without children. Finding people in a similar situation to yourself can be invaluable.
Good luck!