In 1950s Christchurch, New Zealand, a 14-year-old girl from a working-class family, Pauline Parker (Lynskey), befriends the more affluent English 15-year-old Juliet Hulme (Winslet) when Juliet transfers to Pauline's school. They bond over a shared history of severe childhood disease and isolating hospitalizations, and over time develop an intense friendship. Pauline admires Juliet's outspoken arrogance and beauty. Together they paint, write stories, make Plasticine figurines, and eventually create a fantasy kingdom called Borovnia. It is the setting of the adventure novels they write together, which they hope to have published and eventually made into films in Hollywood. Over time it begins to be as real to them as the real world. Pauline's relationship with her mother, Honora, becomes increasingly hostile and the two fight constantly. This angry atmosphere is in contrast to the peaceful intellectual life Juliet shares with her family. Pauline spends most of her time at the Hulmes', where she feels accepted. Juliet introduces Pauline to the idea of "the Fourth World", a Heaven without Christians where music and art are celebrated. Juliet believes she will go there when she dies. Certain actors and musicians are "saints" in this afterlife.
During a day trip to Port Levy, Juliet's parents announce that they are going away and plan to leave Juliet behind. Her fear of being left alone makes her hysterical, culminating in her first direct experience of the Fourth World, perceiving it as a land where all is beautiful and she is safe. She asks Pauline to come with her, and the world that Juliet sees becomes visible to Pauline, too. This is presented as a shared spiritual vision, a confirmation of their "Fourth World" belief, that influences the girls' predominant reality and affects their perception of events in the everyday world.
Juliet is diagnosed with tuberculosis and is sent to a clinic. Again her parents leave the country, leaving her alone and desperately missing Pauline. Pauline is desolate without her, and the two begin an intense correspondence, writing not only as themselves, but in the roles of the royal couple of Borovnia. During this time Pauline begins a sexual relationship with a lodger, which makes Juliet jealous. For both of them, their fantasy life becomes a useful escape when under stress in the real world, and the two engage in increasingly violent, even murderous, fantasies about people who oppress them. After four months, Juliet is released from the clinic and their relationship intensifies. Juliet's father blames the intensity of the relationship on Pauline and speaks to her parents, who take her to a doctor. The doctor suspects that Pauline is homosexual, and considers this a cause of her increasing anger at her mother as well as her dramatic weight loss.
Juliet catches her mother having an affair with one of her psychiatric clients and threatens to tell her father, but her mother tells her he knows. Shortly afterward, the two announce their intention to divorce, upsetting Juliet. Soon it is decided that the family will leave Christchurch, with Juliet to be left with a relative in South Africa. She becomes increasingly hysterical at the thought of leaving Pauline, and the two girls plan to run away together. When that plan becomes impossible, the two begin to talk about murdering Pauline's mother as they see her as the primary obstacle to their being together. As the date of Juliet's departure nears, it is decided that the two girls should spend the last three weeks together at Juliet's house. At the end of that time, Pauline returns home and the two finalize plans for the murder. Honora plans a day for the three of them at Victoria Park, and the girls decide this will be the day. Juliet puts a broken piece of brick into a stocking and they go off to the park. After having tea, the three walk down the path and when Honora bends over to pick up a pink charm the girls have put there, Juliet and Pauline bludgeon her to death.
In a postscript, it is revealed that the next day Pauline's diary was found in which the plan for the murder had been outlined which led to Pauline and Juliet getting arrested. The two are tried, convicted, and sentenced to prison. It is a condition of their eventual release that they never meet again.

Question: What did Pauline and Juliet bond over when they first met?
Answer: Childhood diseases and being hospitalized.
Alternative answer: Sharing stories of childhood hospital stay and severe childhood diseases