Theseus and Hippolyta represent the one strong couple in the play; however, just like all couples, they complement each other. Theseus represents the more emotional, sensual side of the couple, while Hippolyta represents the more rational side of the couple. Even though they complement each other as two opposing sides of the couple, they actually never quarrel even when they display a difference of opinion.
We see in the very opening scene that Theseus is the more emotional, sensual member of the couple and that Hippolyta is more rational. Theseus expresses that he is pining for their wedding day. They are waiting to wed when the new moon appears because a new moon represents a new start. Theseus expresses that waiting for the full moon to change to a new moon is feeling like an eternity, as we see in his lines, "Another moon; but, O, methinks, how slow / This old moon wanes! She lingers my desires" (I.i.3-4). His reference to his sexual desires and how impatient he feels shows us that he is the more emotional and sensual member of the couple.
In contrast, Hippolyta responds with very rational advice, reminding him that four days will pass very quickly when one sleeps away the nights and that one will quickly "dream away the time" (8). While she is not being quarrelsome in these lines, she is certainly expressing her own opinion; plus, she is sharing her opinion in an effort to comfort her betrothed, showing us that Hippolyta and Theseus do not quarrel in this scene.
Another moment in which they express a difference of opinion but still do not quarrel can be found in the final scene of the closing act. Hippolyta remarks that the two couples' account of what happened to them in the woods is strange, and Theseus discounts their stories as imaginings, as we see in his lines, "More strange than true. I never may believe / These antique fables, nor these fairy toys" (V.i.3-4). He even goes so far as to denounce the imaginings of all lovers and poets, calling lovers and poets lunatics and madmen. Theseus's response shows us, once again, that Theseus is the more emotional, maybe even the more irate member of the couple. However, Hippolyta, always the rational and sensible one, responds by pointing out that the consistency of their stories bares witness to the truth of their stories, showing that their stories are man than "fancy's images" (26). Again, while they express a difference of opinion in this scene, they do not actually quarrel. Instead, their debate is dropped as soon as the four lovers appear.