I would actually argue that both Romeo and Juliet have very formal relationships with their parents that are customary of the time period. During this time period, children were expected to be completely obedient to their parents and the relationships were more distant. However, both Romeo's and Juliet's parents show that they care very deeply for their children.
We especially see Romeo's parents demonstrate how much they care about their son in the very first scene. After Prince Escalus has successfully put an end to the whole-city brawl that the Capulets and Montagues have started, we see Romeo's mother ask Benvolio if he has seen Romeo that day and express how glad she is that Romeo was not involved in the fight, as we see in the lines, "O, where is Romeo? Saw you him to-day? / Right glad I am he was not at this fray" (I.i.112-113). We also see Lord Capulet express concern for his son's state of mind, informing Benvolio that Romeo has been seen many times crying at dawn in a certain part of town, presumably the side of town where Rosaline lives, as we see in the lines:
Many a morning hath he there been seen,
With tears augmenting the fresh morning's dew,
Adding to clouds more clouds with his deep sighs. (127-129)
The line, "With tears augmenting the fresh morning's dew," shows us that he is adding to the wetness of the morning with his own tears. We further learn that Lord Capulet has tried to get Romeo to tell him what is wrong and encourages Benvolio to try and find out. Since Lord Mercutio is so concerned about Romeo's state of mind, it shows that, while their relationship may be formal in accordance with the times, their relationship is genuine in that both his father and his mother genuinely care about Romeo.
In a similar way, we also learn that Lord Capulet genuinely cares about his daughter, as well as her feelings. In the second scene, when we see Paris ask him for his daughter's hand in marriage, and not for the first time, one of the things Lord Capulet tells Paris is that his own concession to the match is only half of what is required. He will only concede to the match if Juliet agrees as well, as we see in the lines:
But woo her, gentle Paris, get her heart;
My will to her consent is but a part.
An she agree, within her scope of choice
Lies my consent and fair according voice. (I.ii.16-19)
Hence, since we see that Capulet genuinely does care about his daughter's feelings and wants her to be truly happy, we can say that he sincerely cares about her, even though the relationship is customarily formal. True, we do witness Capulet explode and threaten to disown her when she refuses to marry Paris later, but we must remember a couple of things: 1) He changes his mind about having her married soon because he is worried about her state of grief and thinks it will protect her health; and 2) Complete obedience was expected of children in this time period and she has shown him total respect up until this moment. Hence, we can say that what we witness is a result of his being shocked by her actions and his temper. Therefore, while their relationship is a formal one and possibly on shaky ground, he genuinely does care about his daughter.
Juliet's relationship with her parents is strained; observe, for instance, the way her father treats her when she initially refuses to marry Paris. Her relationship with her mother is hardly better. For most of the play, it is the Nurse whom Juliet confides in, and as stipulated in their first conversation, it was actually the Nurse who breast-fed Juliet as a baby. It was not uncommon for parents to have distant relationships with their children during the middle ages, as child fatalities were common (illness) and it was less emotionally risky to maintain a cold disposition towards one's kin.
Romeo's relationship with his parents is, however, better. They worry about his emotional health when he laments over Rosaline (Act I), and Lady Montague dies of grief when she learns of Romeo's suicide at the end of the play.
However, keep in mind that while Romeo's relationship with his parents is better than Juliet has with hers, both characters suffer from a lack of communication with their elders (along with everyone else). It is this failure to communicate which is one of Romeo and Juliet's main themes, and perhaps the most significant contributor to the ultimate tragedy of the play.
Both of them have a troubled realtionship with their parents because of the rivalries betweenthe two families even before in a way-or trying to explain simply it could be said they are pacifist- and this tention is hightened after juliet realizes her parents would never let them marry causign their tense realitionship to become ones of bitter hatred and confusion.
a very distant relationship.