Jeannie was the pregnant wife of the Joker.
Jeanie was married to Joker when he worked as a chemist at the Ace Chemical Processing Plant. He eventually quit his job in order to pursue his dream of being a stand-up comedian but failed miserably. As a result, he and Jeannie lived in a run-down apartment in a bad neighborhood. Tensions grew between the two and he became very worried about how he would provide for his family. Nevertheless, Jeannie remained optimistic and reassured him that they would find a way, while she laughed at one of his jokes.
Desperate to support his wife and unborn child, the man agreed to help two mobsters break into the chemical plant where he was formerly employed. However, Jeannie soon found out and managed to convince her husband at the last minute to back out of the plan. Unfortunately, just as the man met with the criminals, the police contacted and informed him that Jeannie and their unborn child, whom the man had believed to be a baby boy, died in a household accident.
Stricken with shock and grief, the man attempted to back out of the plan, but the criminals strong-armed him into keeping his promise. As soon as they entered the plant, however, they were immediately caught by security and a shoot-out ensued, in which the two criminals were killed. As the engineer tried to escape, he was confronted by Batman, who investigated the disturbance. Terrified, Joker stumbled backward over a rail and plummeted into a vat of green chemicals. When he surfaced in the nearby reservoir, he removed the hood and saw his reflection: bleached chalk-white skin, ruby-red lips, and green hair. Those events, coupled with his other misfortunes that day, drove the engineer completely insane, and resulted in the birth of the Joker.
Background Information and Notes
If the information provided by the Joker's sometimes distorted memories was to be considered canon, then it was the random death of Jeannie and their unborn child which essentially drove the man to insanity. Later in Batman: Gotham Knights #54, the Riddler approached the Joker for protection against Hush by stating that he witnessed a corrupt police officer, Oliver Hammet, set a fire that resulted in Jeannie's death, rather than the electrical kitchen accident that Alan Moore originally presented. With the newfound information of the man who killed his wife and unborn child, the Joker wanted nothing more than to find the man and kill him.
In Batman Confidential, the Joker's early years were completely retold, that time through Batman's point of view. There was no mention of the Joker ever having had a wife and his lifestyle choices (as documented by Batman) certainly didn't support that one.
Although she didn't appear in Batman: Under the Red Hood, Jeannie was indirectly alluded to in Batman's flashback of his encounter with the Red Hood (The Joker) at Ace Chemicals, where the man was seen begging for Batman to spare him, claimed that he was set up, and that he was not a crook.