Charlie and Renée are Bella's parents, and their marriage didn't last long. Renée hated Forks, and just a few months after Bella was born, Renée left for Phoenix and took baby Bella with her. While Bella gets her quiet, solitary nature from her dad, we're thinking she inherited the love for the sun from her mom.
Both Charlie and Renée are loving, but they express it in different ways. Charlie gives Bella plenty of room; he's a conversation minimalist. He's not around a whole lot, being police chief and all. When he is around, both he and Bella's awkwardness comes out in full-force. Charlie's care for Bella comes through in the little things he does for her, for which he never asks any credit. Although he's unsure exactly how to be a father to a teenage daughter, he tries hard to please his daughter. When Bella has to lie to him in a cruel way at the end of the novel, it nearly breaks her heart, though it seems he forgives her when she returns to live with him in Forks.
In contrast to the somewhat awkward relationship between Bella and Charlie, Bella gets along well with her mother. Bella only left Phoenix so her mother wouldn't stick around for her, losing her love life in the process. Since we only see Renée in one scene at the end of the novel, we have to trust what Bella tells us about her. According to Bella, Renée is scatterbrained, fun, spontaneous, and a social person, unlike her ex-husband and her daughter. She likes communication and constant contact with those important in her life, hence her frequent emails to Bella, checking up on her. We get the impression that Bella doesn't mind her mother's somewhat absentminded lifestyle. Bella and her mother probably get along so well because they complement one another.