Ionesco was one of the big dogs of the Theatre of the Absurd. The Bald Soprano is great example of this genre. The characters often speak in non-sequiturs, meaning that they say things that seem kind of nonsensical and random. The dialogue is also purposely full of clichés, which in some ways satirizes the meaninglessness of everyday speech. The play is technically set in a "realistic" middle-class English living room; however, there are a whole lot of "unrealistic" things going on. For one, time is all askew and seems to either not exist at all, or to be an endless loop.
Also, like in many Absurdist plays, the characters can be said to be iconic. Rather than creating psychologically complex characters of realism, Ionesco fills his play with flat, one dimensional characters. Even so, these characters are deep in their own way, because they represent something bigger than they really are. The Smiths and the Martins could be said to represent middle-class couples everywhere. Beyond that, they could represent every human being on Earth.