Jason Church was a terraforming engineer operating from the transport vessel Incunabulum. He was the husband of Lucian Church and father to Paul Church. The Church family were aboard the Incunabulum when the vessel unknowingly set down on a moon infested by Xenomorphs, leading to the death of all but one of its crew and passengers.
Jason, along with the rest of the crew, was captured by the Xenomorphs and taken to their Hive. He perished within, although the exact cause of his death is unknown.
Church's father, along with the rest of his ships members, was ambushed by a group of Xenomorphs on an unknown moon and taken to their hive.
During the early stages of Church's experience inside the hive, the crew were separated from him, including his father. It is unknown what happened to him afterwards, though presumably he died with the rest of the hive.
When Church escaped the hive, he mentioned how he did not bother to look for his father as he did not want to see what the Xenomorphs had done to him.