This is a very interesting question to consider, given the separate realm of each of these characters and worlds. Firstly, I think it is clear that there is an opposition in this play between the world of Athens and the world of the forest. Athens, as is shown by Act I scene 1, is ruled by law, that can often be very harsh in its treatment, as Hermia discovers. Athens is a place that is characterised by the role of reason and logic in how it is managed. Of course, this is sharply contrasted by the forest, where magic, dreams and enchantment rule, and which acts as a kind of arena where human emotions, free from the constraining influences of civilisation, are free to run riot. This is of course highlighted by the four Athenian lovers, whose affections are presented as unshakeable in Athens, until they go to the forest, where a riotous and chaotic change occurs in how they feel about each other.
Secondly, another parallel structure in the play seems to be the way that the Mechanicals and the Fairies balance one another. If we take the kingdom of Theseus in Athens and balance it against the kingdom of Oberon in the forest, we can see that both have their underclass or servants. The Mechanicals of course are planning a play for Theseus to please him, just as the fairies, principally in the form of Puck, try to please Oberon by carrying out his wishes. All of these four separate spheres collide when the lovers from Athens and the Mechanicals from Athens go to the forest and meet with the fairy world, and are changed dramatically as a result.