Jonathan's Mother: Ahinoam, Wife of Saul
Jonathan's mother is named plainly in the text: Ahinoam, daughter of Ahimaaz, the wife of King Saul. The verse beside the list of Saul's sons gives her name and places Jonathan in a royal family with brothers and sisters.
Jonathan's Father: Saul, Son of Kish
The family record in 1 Samuel 14:49–51 answers the question plainly: Jonathan's father was Saul, and Saul's father was Kish. The narrator sets that line inside an account of Saul's wars, tying the house to its military leadership.