This is Ted's situation.
Birth Abroad to One Citizen and One Alien Parent in Wedlock
A child born abroad to one U.S. citizen parent and one alien parent acquires U.S. citizenship at birth under Section 301(g) of the INA provided the U.S. citizen parent was physically present in the United States or one of its outlying possessions for the time period required by the law applicable at the time of the child's birth. (For birth on or after November 14, 1986, a period of five years physical presence, two after the age of fourteen, is required. For birth between December 24, 1952 and November 13, 1986, a period of ten years, five after the age of fourteen, is required for physical presence in the United States or one of its outlying possessions to transmit U.S. citizenship to the child.) The U.S. citizen parent must be the genetic or the gestational parent and the legal parent of the child under local law at the time and place of the childâs birth to transmit U.S. citizenship.
I am a retired FSO who held a consular commission. I also had a child born abroad while being posted at an Embassy. The applicable FAM reference is 7 FAM 1131.6-3 Not Citizens by âNaturalizationâ
Section 101(a)(23) INA (8 U.S.C. 1101(a)(23)) provides that the term "naturalization" means "the conferring of nationality of a state upon a person after birth, by any means whatsoever." Persons who acquire U.S. citizenship at birth by birth abroad to a U.S. citizen parent or parents who meet the applicable statutory transmission requirements are not considered citizens by naturalization.
They are citizens by statue thru derivative citizenship.