Emily is Briony, Cecilia, and Leon's super delicate mother. She suffers from migraines and spends a lot of her time lying in her room, letting her mind drift. She also spends a certain amount of time feeling bad about not being able to do more. In her dreaminess and her guilt, she's quite a bit like her daughter, Briony.
Emily loves Briony, and has mixed feelings about Cecilia, whose education and restlessness she seems to resent. Her relationship with Cecilia breaks down completely when Emily supports Robbie's prosecution.
Jack is Briony, Cecilia, and Leon's father. He's absent from home in the early part of the novel, partly because he's involved in the government which is preparing for war, partly because he's having an affair, and partly because it just seems like he wants to be.
Leon is Briony and Cecilia's older brother and an all around nice guy. "In Leon's life, or rather, in his account of his life, no one was mean-spirited, no one schemed or lied or betrayed" (1.9.66). This is, presumably, how he is able to be friends with that toad Paul Marshall.
Unfortunately, the stories Leon tells himself about the loveliness of everyone aren't any truer than the stories Briony tells herself. And when they prove false, he's lost. He doesn't help Cecilia defend Robbie, causing her to break with him permanently.
Jackson and Pierrot are Lola's nine-year-old twin brothers who join her in visiting the Tallis family. They're both somewhat traumatized by their parents' divorce and being away from home—Jackson so much so that he wets the bed.
We meet Pierrot again, some sixty years later, after Jackson has died. He has become quite close with Briony.
Pierrot's grandson. He organizes Briony's 77th birthday party.
Emily's sister; Lola, Jackson, and Pierrot's mother. She's dramatic and irritating and leaves her husband to pursue her bliss. Kind of an early hippie. She's not really in the story per se, but she still drives Emily crazy. We a little bit like her for it and a little bit think she sounds pretty awful.