The story is told from a third person limited point of view. This is important because it keeps the suspense alive for the reader. This particular mode of telling events keeps the reader at the same level of information as the characters. For instance, we find out that Missie Mae has been unfaithful at the same time her husband surprises her and finds out.
I am not sure if I would insist on pointing to a human character as the protagonist in this story. Remember that the story was written (or perhaps published) in 1933 when America was galloping straight into the Great Depression. The stock market crash in the US was in 1929. If you are not bound to making an argument that the protagonist is either husband or wife, you could argue that it is money. After all, money holds a lot of power in the text and alters the course of events. The motive for Missie's infidelity is greed. Since the couple ends up forgiving each other in the end and staying together, it seems that Hurston, the Anthropologist, also pointed to the egalitarian and strength of the African American marriage that money could not break.