The "Who's who?" motif
Sometimes in theater, actors will perform as multiple actors in the same play, so there's a funny motif in many plays (and in this one) where the characters make mistakes about who's who after all. Consider Horace never quite figuring out who Arnolphe was anyway, still thinking even in the final act that Arnolphe is this other guy. The hero literally doesn't even notice which guy is the villain. Arnolphe didn't know who Agnès's father and aunt were. That's the villain not realizing who the heroes are. This is a funny motif. It's as if the characters are blind to their own roles in their own stories.
The archetypal interpretation
Arnolphe is a villain who behaves with malice because he is scared of being unloved. He chooses to control his environment by misusing people and by lying to people, and he ends up becoming the dragon who holds the maiden against her will. These are archetypal figures. That means that Horace might represent the hero who saves his beloved from the hands of a cruel and misogynistic man. His father represents divine authority who shows up at the very end to settle the matter indisputably, giving his daughter to the good man and not the villain.
The tragic fall of Arnolphe
It's unmistakable; Arnolphe's story is tragic. He spent enormous amounts of money to get exactly the kind of girl he wanted, just to have her resent him (as she should, one would sort of have to assume). This is a little version of the big tragedy that happens in the story arc. Crysalde warns Arnolphe that if he doesn't change his plans and his behavior, that he will fail and that things will go very badly for him. Yet he insists on his evil and malicious plan. This is his hubris. In the end, his hubris causes him to be left alone and embarrassed.
The good marriage and the bad marriage
One way to interpret the story thematically would be to view Arnolphe as a failed man with intentions to circumvent his failure by brainwashing and kidnapping an innocent girl, to use her and to contain her, to get what he wants from her by any means necessarily. This would constitute a bad marriage or even an anti-marriage. But then consider that Horace and Agnès feel like soul mates. Horace walks right into harms way for his beloved. He faces Arnolphe. He helps Agnès while she's in duress. Then, when the parents show up, he wins her hand in marriage with their parents' approval and joy. This is a good marriage. Horace is a hero for this.
The motif of visitors
When visitors show up to Arnolphe's house, it often goes poorly for him. For instance, Chrysalde confronts Arnolphe for his vicious behavior. Then again, bad news comes from a visit when Arnolphe realizes that Agnès likes Horace. Again, there is bad news when Horace comes to save Agnes from "Monsieur de la Souche." Finally, the rouse ends when the young couple's parents pay Arnolphe a final visit to put an end to it. This underscores Arnolphe's paranoia and his knowledge that he is doing something wrong. He feels shamed, and he associates other people with his misfortune.
