My grandson was born in London to an American father and an English mother. Son went to US consulate that day to register his son’s birth as an American natural born citizen and a US citizen passport was issued to my grandson that day. His mother also registered his birth as a British citizen that day. When grandson comes to this country, he gets in the US citizen line for entry just like all other US citizens.
My son was born in 1963 in Germany in an American military hospital. When he was six weeks old we took him to the American Consulate in Munich, Germany to get him registered. He received an American birth certificate and also an American Passport. The same thing also was true for our daughter who was born in the same same hospital in 1970. We took her to the American Consulate in Munich to get her registered. She received her American birth certificate and her American Passport.