Hmm first off, only the active duty personnel is required to get shots. family is not, even if you go overseas. You do not have to do shots even for DoD schools, religious exemptions are accepted at all time (you might have to fight a little and point out regs, but the law is on your side).
We decided on very delayed and selective vaccines, and the military doesn't know about them. Because they are all or nothing, and I mean CDC schedule, not just your state's requirement. Which means a 12 year old girl needs to get Gardasil or you cannot come along overseas. It is crazy and I would never ever consider anything but an exemption since you have no choice in delaying or selecting if you vaccinate with the military.
It very much depends on the country you might be going down the road, so there is no need to jump the gun now. What if you are sent to Great Britain or Germany? Absolutely no need. the only thing you might consider is a single measles shot which is available in Europe cause there are large pockets of unvaccinated children if you are afraid of measles. And you can do that privately, out of pocket, nobody needs to know.
As for your DH being e.g. in Iraq - they do get screened and heavily looked at before they come back. There is no need to worry. He won't bring back anything that's contagious that isn't around here too VPD-wise. Especially since he is required to be up to date. And they check for MMR and chickenpox titers, not just vax records in the Air Force. So you will know for sure that he is immune.
Beware though that active duty gets a yearly Flumist shot at most bases. We avoid the issue by getting a single dose dead virus shot at the health department ($20) so DH doesn't shed. When I called around last week to track one down, the obgyns office got all frantic that they want to give Flumist to a husband of a pregnant woman. They literally freaked out and said HE** NO. But, as always, the shot clinic on base says whatever you get it or we kick you out. Not mentioning that you can get it off-base at any time though.