The reader does not know much about Romeo's parents. They are not really in the play. Montague gets fewer than a dozen lines over the course of the entire play. What the reader or viewer learns about Romeo's family is from Romeo himself. The fact that Romeo spends more time with Friar Laurence and seeking his advice is an indicator that Romeo is not that close to his parents. Another indicator of this is that Romeo is very willing to throw away his family name in order to be with Juliet. He comes from a wealthy, respected family, so being that willing to give up the name means it must not mean much to him in the first place. "Henceforth I shall never be Romeo...My name, dear saint, is hateful to myself / Because it is an enemy to thee" (2.2).
Juliet's relationship with her parents is much better, at least at the start of the play. Paris asks Capulet if he can marry Juliet. Capulet's response is yes, but wait, and only if she agrees to it. That's a fairly nice gesture since it is well within Capulet's power to simply tell Juliet who she will marry and when (which is what happens like two days later). Before the party, Juliet's mom asks Juliet to keep an open mind about Paris and talk to him at the party. Juliet agrees. She listens to her mom and agrees to follow directions. Solid relationship.
Of course all of that changes when she meets Romeo and falls in love. Then she doesn't listen to a word her parents say. She marries behind their backs and tells her father that she will not marry Paris no matter what. Capulet hits her and tells Juliet to leave his sight. That's a quick turn around from the happy and content family a few days earlier.