Yes, from what you describe and according to U.S. law, your children are U.S. citizens at and from the time of their birth and are NBC’s and eligible to hold any office in the US including POTUS.
That's incorrect. U.S. military installations abroad are not considered U.S. soil for the purposes of citizenship. The following text is from the State Department's Foreign Affairs Manual.
7 FAM 1113 NOT INCLUDED IN THE MEANING OF “IN THE UNITED STATES”
c. Birth on U.S. Military Base Outside of the United States or Birth on U.S. Embassy or Consulate Premises Abroad:
(1) Despite widespread popular belief, U.S. military installations abroad and U.S. diplomatic facilities are not part of the United States within the meaning of the 14th Amendment. A child born on the premises of such a facility is not subject to U.S. jurisdiction and does not acquire U.S. citizenship by reason of birth.
With all due respect BuckeyeTexan; I believe you are incorrect in your interpretation of that manual. What that manual is addressing are the children of foreign nationals, i.e. non U.S. citizens who work at U.S. military installations or U.S. diplomatic facilities abroad or who otherwise give birth to children on the grounds of a U.S. military base or U.S. embassy or diplomatic facility. Such children of foreign nationals born on the grounds of a U.S. military or a U.S. diplomatic facility are not considered having been born on U.S. soil for purposes of being considered born an American citizen as they are not subject to the jurisdiction of the United States of America.
Citizenship at Birth for Children Born Outside the U.S. and its Territories
As Ax and his spouse were BOTH U.S. citizens at the time of their children’s birth AND Ax was an active duty U.S. military service member, his children meet the requirements of U.S. citizen at birth; his children are considered to be U.S. citizens from the time of their birth, no different if they had been physically born on U.S. soil, regardless of what country Ax was serving in at the time and whether or not they were born on a U.S. military base or not. There is a requirement to register the birth through the U.S. consulate but that is AFAIK routinely done for U.S. service members whether their children are born on base or even off base in a private non-U.S. military hospital. Their physical place of birth is not the determining factor here, it is the citizenship of the parent or parents and other factors such as how long one or either of the parents resided in the U.S.
Please read this BuckeyeTexan as the last FAQ addresses the very same question that the manual you referred to was addressing:
Q: I was born to a non-American mother inside a US embassy compound during civil strife in my home country. Am I an American citizen?
A: No. US diplomatic or consular facilities abroad and US military installations abroad are not part of the United States within the meaning of the 14th Amendment. A child born on the premises of such a facility is not born in the United States and does not acquire US citizenship by reason of birth there.
In other words, the a child of a foreign national who may happen to be born on the premises of a U.S. facility overseas while their non-U.S. citizen parent(s) are present there and provided they do not meet any of the requirements of U.S. citizenship, i.e. having at least one U.S. parent…etc., such as in the case of a foreign national(s) working there as an employee, there seeking refuge in due to political strife, or there in the process of requesting asylum in the U.S., is not considered to be born an American citizen by virtue of having been born on a U.S. facility overseas as this is not the same as having been born on U.S. soil. This is very much quite different however from Ax’s and his children’s’ situation as my previous link explains it quite clearly.
The same sort of rules apply to the children of foreign diplomats serving in the U.S. – the children of foreign diplomats born to them while they are serving in the U.S. in the capacity of being registered foreign diplomats, are not considered U.S. citizens at birth by virtue of them having been born on U.S. soil and neither are children born of parents on temporary visitor visas (vacationers) as they are not subject to U.S. jurisdiction.
The same applies to U.S. citizens temporarily travelling or working abroad. If I, for just one example, am a U.S. citizen working for a U.S. company overseas working on a DOD contract for instance, I have not applied for or established permanent residency there, nor have I applied for citizenship in that foreign country, any of my children born overseas are U.S. citizens at birth providing I have met the U.S residency requirements and I register the birth of my child at the U.S. consulate, that child born overseas is a U.S. citizens from birth and no different as if they had been born in Lancaster PA.
The same would apply if I was a U.S. citizen vacationing in France on a temporary visitor visa and gave birth to a child while I was there. As long as I had met the U.S. residency requirements and registered the birth with the U.S. consulate, my child would a U.S. citizen at birth and not a French citizen.
FRiend, you have no idea what you’re talking about. That section of the FA manual is not addressing only the children of foreign nationals. It deals with ALL claims of citizenship on U.S. soil.
It goes on to define what, exactly, is considered U.S. soil. It gets so specific that it defines when birth on a military vessel is considered birth on U.S. soil. (BTW: international waters = no.)
Yes, Ax’s children are citizens at birth. No one is disputing that. According to the State Dept., that does not, however, automatically grant them eligibility under the Constitution for the presidency. The courts have not ruled on the eligibility of those granted citizenship at birth by statute.