Sometime before the events of Beyond Good & Evil Jade's father, whose real name is not known, is the father of Jade and the husband of Jade's mother. Up until the events of Beyond Good & Evil, it was unspecified that he was a very close friend of Pey'j, and along with him, they constructed the Beluga. As a result of unelaborated problems with the authorities on their home planet, he and Jade's mother entrusted their daughter to Pey'j.
It is unknown what became of Jade's parents after Jade and Pey'j left their planet, whether they are still alive or not, or if their 'problems' caught up with them. The authorities and problems Pey'j mentions also are not expanded upon, one can assume they were all part of the IRIS Network or another rebellion organisation, working against a corrupt government on their planet, and judging by how Hahn mentions the DomZ and the Alpha Sections deceiving and corrupting previous planets, this is very feasible, however this is only speculation and not solid fact.