You've gotten some great ideas and suggestions (umbrella homeschooling groups can be wonderful sources of material, socialization, and deeper education).
Another thing to bring up is that you'd like to see your children have continuity and consistency in their education, because those things are proven to help children succeed both in continuing education and life in general. Since you're military, it's very likely that you'll be stationed elsewhere again in a year or two, which will mean disrupting their education. As a child that went through many, many moves to different school sytems, I can definitely tell you I did not get the education my less-frequently moved peers did. There were large gaps in my cirriculum, and things I covered so many times I was bored to tears (I was "taught" the book "The Scarlet Letter" 8 times in high school, for example, but had never read many of the other classics). This type of gap left me at a huge disadvantage for things like the SATs, foreign language, etc.
Homeschooling your children would allow you to keep continuity of education, ensuring that moving around so much doesn't interrupt their learning. Your cirriculum, their schedules/classes, and their progress wouldn't be interrupted and changed with every move.
There have actually been resolutions and bills debated to address just such problems, so it's pretty easy to verify that even the US government believes that military children are often at a disadvantage in education due to frequent moves. Homeschooling could help alleviate that.
"This isn't life in the fast lane, it's life in oncomming traffic." -Terry Pratchett