Military bases are not US soil, and neither are consulates or embassies - that is a common misunderstanding. The embassy is technically under the jurisdiction of the host country, but is afforded special privileges, such as immunity from most local laws.
Regardless of where your parents are from, if you are born in the US, you are a natural born citizen (don't ask me about US territories).
If not born in the US, it becomes more complicated. If one of your parents is a US citizen and the other is not, the US parent must have been physically in the US for at least 5 years, two of which after reaching the age of 14.
This does not need to be consecutive, nor did the parent need to reside or be domiciled here.
There are several exceptions to the above, based on certian locations. I also do not know the requirement if both parents are US citizens, nor do I fully understand the rules for a parent who is a US national but not a US citizen.
In that case, either look up the law or consult an immigration attorney.