Very differently from what might be seen as a contemporary ideal. By that I mean, Montague knows his son Romeo has upset about something early in the play, but Romeo won't talk to him. Late in the play Lady Montague dies of grief from losing her son. We know, then, that Romeo's parents care for him, but no, there is no sense that he can (or will) talk to him.
The Capulet situation is similar. Lord Capulet loves his daughter, and resists marrying her to Paris at first because she's so young, and so dear to him. Lady Capulet does talk with Juliet about marriage, but marriage with Paris. Lord Capulet sees Romeo behaving himself well at the party, and so is willing to not attack him, but in general, the distance between parents and child is extreme, largely due to the feud between families.