I don't have first hand knowledge about adopting/fostering while in the military, but since Im a civilian federal employee, I came across information when I was doing some research. I know that if you are on active duty in the military, you are eligible for reimbursement of expenses up to $2,000 for the adoption of a single child and up to $5,000 per family per year. There is one caveat: The adoption must have been arranged through a non-profit agency, whether they are infant adoptions, intercountry adoptions, or adoptions of children with special needs. I also know there have been some improved leave benefits as well (
http://www.senate.gov/~bennelson/news/details.cfm?id=250145&&) Under the military’s Program for Persons with Disabilities, military parents may be eligible to receive up to $1,000 a month for disabled or special needs adopted children. The military also has a program called the Exceptional Family Member Program that will ensure that adoptive parents of special needs children are assigned to bases or duty stations that can meet the needs of the child.
As for fostering, I think you need to contact some local agencies and see if they are willing to work with you. There are no rules preventing you from becoming foster/adoptive parents just because you are military.