What is the relationship between Romeo and his parents in Romeo and Juliet?

What we know about the Montagues and their son must largely be surmised from Romeo's actions.  There is not the intense dialogue from Lord and Lady Montague as there is between the Capulets and Juliet.  In fact, Montague has only ten lines of dialogue in the entire play!  (See link below.)

We know that Romeo does not hold the anciet animosity for the Capulets that his parents cling to.  When Juliet asks him to "Deny thy father and refuse thy name," Romeo does not hesitate to respond with "Henceforth I shall never be Romeo...My name, dear saint, is hateful to myself / Because it is an enemy to thee" (2.2)

The fact that Romeo is so willing to give up his "good name" is pretty telling of his relationship with his parents.  They have not given him much reason, in his opinion, to value his family ties. 

Romeo and Juliet are supposed to hate each other; their families have an "ancient grudge" between them, and these two young people are expected to continue the cycle of hate. The two realize this predicament from their first moments of falling in love. After their first kiss, Romeo is told that Juliet is a Capulet and laments, "Is she a Capulet? / O dear account! My life is my foe's debt." Juliet also seeks to learn the name of the man whom she's just kissed, and when her nurse returns with this information, she is dismayed: "My only love sprung from my only hate!" Despite the fact that they have been raised to view the other family as a "loathed enemy," Romeo and Juliet quickly fall in love.

Throwing aside their families' expectations, Romeo and Juliet make their own independent plans. They marry in secret just before Romeo is banished for killing Juliet's cousin. This complicates their relationship, but Juliet eventually makes plans to join Romeo, leaving behind her comfortable lifestyle and the support of her family. Lord Capulet expects Juliet to marry Paris, and when she refuses, Juliet's father calls her a "disobedient wretch" and tells her that if she doesn't, she can "hang, beg, starve, die in the streets." Juliet's loyalty has shifted from the Capulet family to Romeo, and she is willing to risk this fate in order to be with him. Thus, she undertakes a risky plan to fake her own death in order to be with Romeo.

Although the two are young, they are bold in their actions, determined to find a way to be together despite the expectations of their parents. In the end, their love demonstrates the need for their parents to bury the long-standing grudge that exists between the two families.

The relationship between Romeo and Juliet can be largely defined as the passionate, all-consuming first “love” of two relatively naive teenagers, as that is what the characters are. Juliet is 13 years old (Act 1, scene 2, line 12), and assumedly, Romeo is not much older. And while Juliet is advised by her mother to begin thinking very seriously about marriage, both her and Romeo are very inexperienced in romance. Romeo is initially infatuated with Rosaline, whose lack of reciprocating feelings causes him to be morose and cynical about “love” on the whole (Act 1, scene 1, lines 189-197), which reveal his affection and understanding of love revolve more around the concept of “love” rather than on a specific person. Romeo and Juliet fall in love entirely on appearances, with Romeo completely snapping out of his previous grief, claiming “Did my heart love till now? Forswear it, sight! For I ne’er saw true beauty till this night.” (Act 1, scene 5, lines 54-55). Juliet experiences a similarly quick reaction, as she says to Romeo, “My ears have yet not drunk a hundred words of thy tongue’s uttering, yet I know the sound.” (Act 2, scene 2, lines 58-59). And despite her recognition of the unadvisable quickness of their affections in lines 117-118 in Act 2, scene 2, “...I have no joy of this contact tonight. It is too rash, too unadvised, too sudden…” Juliet and Romeo’s love continues to overshadow everything else.  Juliet proclaims, “if all else fail, myself have power to die,” in answer to her possible marriage to Paris, indicating her desire to die rather than be with someone besides Romeo (Act 3, scene 5, line 244). Juliet’s love for Romeo surpasses her grief over his killing her cousin, Tybalt, as she reconciles, “My husband lives, that Tybalt would have slain; And Tybalt’s dead, that would have slain my husband. All this is comfort…” (Act 3, scene 2, lines 105-107). And while Juliet and Romeo may love with intensity, it’s still a very immature, illogical love. This is evidenced in Romeo’s actions after his banishment, when he weakly attempts to stab himself. As the Friar states in lines 117-118, Romeo failed to think of how his suicide would have affected Juliet. The blinding nature of their loves, coupled with their relative inexperience, culminates in their eventual suicides, spurred by Romeo’s failure to control his emotions in the wake of hearing of Juliet’s “death.”

Juliet's relationship to Romeo changes throughout the play.  In the beginning, the two do not know each other, but are enemies by virtue of the hatred that their respective families share.  They meet toward the end of Act 1; after that meeting, they fall madly in love (or in lust, depending on who you ask!) and their relationship changes to one of infatuated teenagers.

When they agree to, and carry out, a secret wedding the following day, their relationship changes once more to that of husband and wife.  Unfortunately, other than consummating the marriage, they have little interaction as husband and wife.  After Romeo kills Juliet's cousin, Tybalt, to avenge Tybalt's murder of Romeo's best friend, Romeo and Juliet move to extremely-forbidden lovers.  After a night spent together, they must depart, as Romeo is now banished from the town in which both were raised. At this point, their relationship changes to that of separated lovers.  

The Friar works with Juliet to hatch a plan to return the duo to each other, but, unfortunately, the plan does not work.  In the end, they end up killing themselves -- here, they are both partners in a double suicide. Thus, the relationship between Romeo and Juliet evolves and morphs several times over the course of their several-day courtship, marriage, and death.

When Romeo and Juliet interact with their parents, those interactions don't seem to be especially pleasurable for the kids or fulfilling for the parents. At the beginning of the play, Romeo's parents try to talk to him about what is bothering him, but they resort to asking Benvolio to intercede and speak with him to try to find out what's wrong. It is Benvolio who is able to get Romeo to talk about his unrequited love for Rosaline, and his parents seem to be totally in the dark.

When Juliet's mother approaches her about the suit of the County Paris, Juliet is pretty noncommittal about her willingness to marry him; she lukewarmly expresses her obedience to her parents in this matter, as in all matters. However, later, when she refuses to marry Paris after Tybalt's death, her father threatens to throw her out of the house, and her mother essentially declares that she doesn't ever want to talk to Juliet again.

Neither Romeo nor Juliet feels comfortable enough to go to their respective parents and explain what has been going on, to ask them for guidance or assistance, and they end up ruining their young lives as a result. Perhaps if their parents had been better listeners (especially Juliet's), the story would not have had to end in tragedy.

In the early scenes of the play, Romeo’s parents show themselves to be loving and concerned parents.  After the families argue and are given the ultimatum by the Prince, Montague expresses his concern about Romeo’s state of mind.  “Many a morning hath he there been seen, / With tears augmenting the fresh morning dew…Away from the light steals home my heavy son, / And private in his chamber pens himself” (Act I, Sc. 1).  Romeo’s father is worried about him, and he wants Benvolio to talk to Romeo. “Black and portentous must this humour prove, / Unless good counsel may the cause remove” (Act I, Sc. 1). The words black and portentous indicate that Montague thinks something will go wrong if they do not help Romeo change his mood.

Romeo’s parents also show their love for him in this part of the play.  After the Prince leaves, Lady Montague asks Benvolio where Romeo is: “O, where is Romeo? saw you him to-day?  Right glad I am he was not at this fray” (Act I, Sc. 1).  Though she is worried about not seeing Romeo, she is also very happy that he was not involved in the earlier conflict between the families.  Montague also expresses his love when he says, “Could we but learn from whence his sorrows grow. We would as willingly give cure as know” (Act I, Sc. 1).  Romeo’s father wants to know what is wrong with his son, but more importantly, he wants to help him get over it. 

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.

The family dynamics of Romeo and Juliet can seem pretty strange to us in the modern day. At this time in Europe, lifespans were much shorter, so people were considered full adults around the time they became teenagers. This meant that they were expected to take on new responsibilities, including marriage and raising a family. Romeo and Juliet's families do want their children to do well in life, but they are more concerned about these two young people fulfilling social expectations than their true happiness.

One thing which may seem especially unusual to us but was quite common in Shakespeare's time is the character of Nurse. Throughout history, wealthy families of Europe would often employ a nurse (also called wet-nurse or nanny) to care for their children. These women would care for the children as if they were their own, breastfeeding infants and serving as confidante in the older years. As we can tell in Act I, Nurse has a lot of affection for Juliet and fulfills the roles her mother does not. Lady Capulet is really more of an administrator for Juliet's appearance in society, hence her desire for Juliet to marry! 

On the other side, Romeo is offered a little more independence than Juliet because he is a boy. He is free to spend time with his male cousins and even wander among the trees by himself while he daydreams. Romeo's parents find his introversion a little odd, but nonetheless want him to do well.

The family roles of the Tudor and Renaissance period did not really allow for the kind of emotional connection most parents and children share today. Only in the most serious of cases would a noble parent step in to discipline their child, and they spent even less time "getting to know" their children. To us, this may seem cold or cruel, but it was the reality of life for wealthy Tudor and Renaissance people.