Were your children issued Certificates of Naturalization? If they weren’t, they’re considered to be Citizens of the United States at Birth.
Definition C in the US Code for Nationals and Citizens of the United States At Birth seems to apply to your family: “(c) a person born outside of the United States and its outlying possessions of parents both of whom are citizens of the United States and one of whom has had a residence in the United States or one of its outlying possessions, prior to the birth of such person;”
Both of my children have a birth certificate issued by the State Department. While I cannot recall the exact phrasing I believe the birth certificates are headed “Record of the Birth of a US Citizen Born Abroad.”