The family members said Thursday night that they received word of Raymond Estelle Jr.'s death Wednesday. He served 20 years in the Air Force.
Military officials have not yet confirmed the death, but relatives said Estelle was one of the people killed at the airport.
Estelle, who lived in Virginia, leaves a wife, a 9-year-old daughter and a 1-month-old son, according to one of Estelle's uncles, who did not give his name.
Estelle, along with seven other airmen and a civilian contractor, were killed when an Afghan Air Force pilot opened fire at the Kabul airport.
A Reuters report was included in this story.