It was as if we got back from the war and were like: "Man, this novel should have an ending"
"Nah...it doesn't need one..."
So, postmodernism essentially just allows people to do weird stuff with books that hasn't really been done before (at least in the era when that book was written, as I'm going to assume the definition of postmodernism changes depending on it's precursor (modernism).
The Poisonwood Bible exhibits more than a few of these characteristics. For one, it is written after the war, and the time period it is reflecting on is the area around 1960, with the Congo's independence being a big deal.
But, postmodernism really is seen in this novel mainly by the use of narrators (and how there aren't numbers to the "chapters," but I' don't think that is nearly as significant). Kingsolver uses multiple narrators in this novel, which adds a form of insight and depth to this particular story, which is not seen very often in the other great literary works from the time period when it was written. While most novels that we cover in our English language/literature and composition classes during school focus on a main character, this book, with it's narrators, doesn't seem to focus on any one person, but rather the sincerity of the family as a whole, which allows the story to gather insight from many more sources than what most novels are capable of. A good example is how multiple people mention the poisonwood tree, and how the novel is able to gain insight from each child and their experiences with the tree, either personal or watching their father handle it like a dumb American.