Lord Capulet (a.k.a. Capulet) is the father of Juliet. At first, he seems like a pretty good dad. When Paris comes sniffing around for thirteen-year-old Juliet's hand in marriage, Capulet puts him of, citing Juliet's young age and even suggesting that he'd like his daughter to marry for "love" (1.2.2-3). This, by the way, is pretty uncommon in Shakespeare's plays. Most fathers (like Baptista Minola in The Taming of the Shrew) broker marriages like business deals, without ever consulting their daughters.
But Lord Capulet doesn't play the good father for long. Paris eventually wears him down and convinces him that he and Juliet should wed (3.4.2). (By this point, Juliet is already be secretly married to Romeo.) The thing is, Juliet's not exactly down with marrying Paris and things get ugly when she tells her father as much.
Lord Capulet's response to Juliet's "disobedience" is so violently harsh that we begin to see him as a bit of a tyrant. We see the physical aggression most prominently in the big, confrontational scene with Juliet over whether or not she will marry Paris. When Juliet refuses, Capulet screams, "Out you baggage, / you tallow face" (3.5.3) and says, "My fingers itch" when Juliet stands up, which may suggest that he's prone to physical violence (3.5.4). He also lashes out against the Nurse and his wife.
Lord Capulet's relationship with his wife is also up for debate. Lady Capulet is probably much younger than he, since she was married to him when she was about twelve years old. Needless to say, this age difference seems to have caused some tension in their marriage. "Too soon marred are those so early made [wives]," he tells Paris, clearly referencing his own wife (1.2.3).