What is the relationship between Capulet and Juliet like?
Capulet's feud with Lord Montague is at the heart of the sorrow Juliet feels in not being able to be with Romeo. Her father's stubbornness is not being able to end the feud is what leads to their deaths. Only in the deaths of the two children can the fathers agree to stop the fighting. Throughout the play, Capulet's relationship with Juliet demonstrates this willful pride and stubbornness. Lord Capulet negotiates her marriage arrangement with Paris. At first he says that his daughter is too young but later consents to the marriage and assumes that Juliet will follow his direction. Marriage is viewed in the time period as a contractual relationship between the father and the suitor with little input from the woman. Juliet has acted on her own feelings in marrying Romeo, openly defying this social convention of marriage. Capulet shows additional disregard for his daughter's emotional reaction to Tybalt's death and Romeo's banishment. He is more concerned with his own social standing and the appearance of a young daughter defying him that he tells Juliet that he will put her out on the street to die rather than tolerate her insubordination. Juliet feigns obedience while plotting her own plan to reunited with Romeo in the tomb. While he is sad when his daughter appears to be dead, he seems more concerned that the wedding plans are ruined and that he his only child has died without leaving him heirs.
The previous answers are very good; I would just like to add a few lines that help to support the argument, particularly to look at Juliet's side of things.
In 2.2.160, Juliet cries, "Bondage is hoarse and may not speak aloud." What she means (according to Brian Gibbons) is that "My being under my father's strict control stops me speaking loudly."
Furthermore, (earlier in the scene, line 35) she pleads with her love, "Deny thy father and refuse they name." In doing so, Juliet is also refusing her name, the "bondage" of her father, and rejecting the long-standing feud.
As for Capulet, he claims to love Juliet, and perhaps he does in his rather old-school way, but her wishes are secondary to the desire to have her marry well and properly. He assures Paris in 3.4.12-14: "Sir Paris, I will make a desperate tender / Of my child's love. I think she will be ruled by me; nay, more, I doubt it not." Capulet has no idea that his patriarchal rule will be ignored and thwarted.