The narrator pretty much sticks to third-person limited, giving us access to Babbitt's thoughts and opinions of the world. Sometimes, the narrator is so close to Babbitt that her/his thoughts almost merge into one consciousness, as you get with lines that show Babbitt's opinions on other people, like, "Littlefield was the Great Scholar of the neighborhood; the authority on everything in the world except babies, cooking, and motors" (3.1.5).
At other times in the book, though, the narrator pulls away from Babbitt and becomes so detached that it sounds like a journalist who's simply writing down the events of Babbitt's life. We get this kind of voice in passages like this:
Which of [Babbitt's friends] said which has never been determined, and does not matter, since they all had the same ideas and expressed them as always with the same ponderous and brassy assurance. (10.3.10)
Here, the narrator is so removed and judgmental that we sense that there is some other character telling Babbitt's story. But this sense of removal always seems to disappear just as quickly as it shows itself, and we zoom in close to Babbitt's brain yet again.
Sinclair Lewis probably chose to give us this dance between an intimate narrator and a removed one because he built Babbitt as a satire that revolves around one specific person. And when you're satirizing someone, you're usually going to sound pretty judgy and removed… that's just the nature of the satire beast.
On the other hand, Lewis' satire of the "typical American man" only works if we become very, very familiar with the ways that Babbitt thinks, which means that we also have to spend a lot of time perching on his shoulder and reading his thoughts like some sort of mind-reading parrot. Ooh. A mind-reading parrot sounds pretty cool. We want one of those.