Here are 2 links that I hope will give you some info on military adoptions. If you go to Google you will also find some other links.
http://www.militaryadoption.com/ http://www.adopting.org/military.html
I don't know much about domestic adoption either. We are pursuing an adoption from China.
My DH is on active duty for the Army National Guard and we will not be transferred out of state. One of his first questions to our adoption agency is whether or not being in the US Army has a negative affect on being chosen as an adoptive family.
Our agency gave us an emphatic NO! that it would not affect us negatively. In fact, being in the military is often looked upon as a plus since you generally have job security and because of the high regard our military personnel have overseas.
So, that's what I know about being a military family adopting internationally. I hope it gives you some perspective.
Best of luck to you!! Happy researching and I hope you find the answers you are looking for!!

__________________
Happily married for 19 years & mommy to 3 beautiful daughters
~13 year old (born preemie @ 24 weeks), 5.5 year old & 3.5 year old (both born in China!)~
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