Charlie prefers life to be simple. He tends to shun confrontation and emotional situations. But since Bella moved in with him, he finds himself in a continual struggle whether to deny the strange occurrences in his daughter's life, or to step up as a father and deal with the half-truths his daughter is dishing up for him. As Jacob puts it, "[Charlie] just likes to pretend things are normal" (25.103). Even after Jacob changes into a wolf in front of him and forces Charlie to face reality, he continues to maintain his policy of "Need to know, only."
Whether his reluctance to face facts points to a weakness of character, or to a sheer fear of what he might find out, Charlie's love for Bella overcomes all pains and struggles. He gives his blessing for her marriage to Edward, although he's had his fair share of misgivings about the guy. He even accepts Bella's new appearance after her transformation and the fact he has suddenly become a grandfather to Renesmee. All he really wants is to see his daughter happy and alive and to have her in his life. His relationship with Sue, the "werewolf" mother, helps ease his transition into his new life, filled with the supernatural.
For more info on Charlie, check out his "Character Analyses" in other books of the Twilight series on Shmoop.