Neither Romeo or Juliet seems to have a close relationship with their parents. Juliet's parents pay little attention to her actions unless it relates to them directly. As evidenced in Juliet's mother's appearance in her rooms.... she was stunned, it was something that didn't happen very often. Her father is a bit different, in that he thinks about his daughter first.... until her wishes do not match his own.... then he puts his foot down.
Romeo's relationship with his parents seems to be a bit more typical of what we would expect. He is a young and finding his own way. They care about him (his father worries about his depression, and his mother worries about his whereabouts), but they also give him a lot of space.