Comedy; Pastoral
In the most basic of terms, The Decameron is an early prose novel, probably the first written in the Italian vernacular. We can call the work as a whole a comedy, even though disease and death are hovering in the background and in plenty of the stories. We can do this because the characters overcome the physical and psychological strain of the epidemic and achieve a level of happiness that they seek in leaving Florence. In this sense, the work has a "happy ending," even though we don't know what will happen to them in the future, and nobody gets married. And of course, there's all the comic material—some ironic, some coarse, some obscene—but all hilarious.
Though the work isn't strictly pastoral in the classical sense, it does invoke the wholesome and curative aspects of nature. No shepherds or shepherdesses in this one, but babbling brooks and dappled sunlight? Check. Birdies and flowers? Check.
We'll also point out that the stories are hugely varied in their genres. You'll see satire, folktales, tragedies, comedies, and fabliaux. You'll have to redefine genre each time you start a new story.