With a history of military background the Jordan family was originally composed by Martin and Jessica Jordan. They had three sons who would follow different paths after the tragic death of Martin.
Jack, the eldest son would married to Janice and had two sons: Jason and Helen (also know as Jennifer). Sadly all the family died in unspecific circumstances involving a supernatural force.
Hal, the second son would join the air force and eventually would join the intergalactic Green Lantern Corps. He is in an off-again-on-again relationship with Carol Ferris. In a possible future he could be parent of Jim Jordan.
Jim, the third son, married to Sue Jordan and had two sons: Howard and Jane. Having discovering the secret of his brother, he choose to stay in Coast City along with his family, taking the testimony of his father.
The Green Lantern isn't the only heroic name associated to the Jordan family. Pre-Flashpoint, the name of Airwave was a heroic moniker used by a cousin of Martin, Larry Jordan and once by Larry's wife, Helen. The son of Larry, also called Hal Jordan, later would too become Air Wave. Post Flashpoint is unknown if the Air Wave branch of the family still exists.