They have the fewest lines of the major characters in the play, but they clearly play the role of concerned parents. When we first meet Romeo after the opening fight, it is after a long conversations between Montague and Benvolio. Montague expresses how concerned he is at Romeo's recent depression, and he asks Benvolio to find out what is going on. In the last scene of the play, we find out that Lady Montague has died of an apparent "broken heart." I always find this awkward announcement of her death strange, but it evens things up so each family in the play loses two members.
Typically, these characters are played with a bit more emotion and edge to them than the Montagues. Capulet certainly has a fiery temper that causes him to lash out at Juliet, his wife, and the Nurse. However, he also clearly holds his daughter on a pedastal. Early on he denies Paris' request to marry her because Capulet does not believe she is ready, and later, Capulet promises his daughter's hand to Paris because he believes he is going to cheer up his family. Lady Capulet seems to put more on Juliet's shoulders, and she wants her daughter to marry Paris and seems to see this as a crowning achievement for the family. She also washes her hands of Juliet quickly after Juliet resists and becomes a bit cold. This rough side is shown again when Lady Capulet plans the murder of Romeo after the fight in Act III with Tybalt.
The Friar looks at Romeo as a young friend, and there he seems to relish his mentor role with him. If you look at Friar's longer speeches and interaction with Romeo and Juliet, he is always giving some sort of advice. The major problem, however, is that the good Friar does poorly in adhering to his own advice. He tells Romeo to move slowly and he wants to bring the families together, but he contradicts this good advice by allowing them to marry quickly and coming up with a plan to trick the families into believing their children are dead.
The Nurse tries to be a mentor to Juliet and sees herself as a mother figure, but she ends up being more of a friend and "yes man" for her instead. There are two problems. First, the nurse lacks intelligence and is shown time and again as a babbling fool with a good heart. Second, she is still a servant of the family, and her bond with Juliet makes her a pleaser instead of a solid friend or mentor.