The plot is far too long to summarize so read it in Wikipedia here. There's a fine commentary on the importance of the book in the Wall Street Journal here. It seems all sources characterize The Betrothed as a romance. To be sure, the ultimately requited romantic love of Renzo and Lucia drives the driving narrative flow but The Betrothed is more than a mere romance or simply an historical novel.
Without an electronic version of the book, I cannot count how often the various protagonists expressed trust in Providence. Suffice it to say, quite a few. In addition, to the best of my recollection, each of Manzoni's positive figures expressed and exemplified that he or she was motivated by the Christian faith. There were even two conversion accounts, one recounted as having occurred in the past of Fra Christoforo and the one of "the Unnamed" narrated in the present. Conversion accounts are always tricky but I believe Manzoni was able to pull off both of them. Not as well done as Brideshead Revisited but still credible.
Providence incarnate, as it were, was personified in the character of Federigo Borromeo, archbishop of Milan. The real Borromeo was the cousin of the sainted Charles Borromeo, whom he succeeded as archbishop. In The Betrothed (and in history) Archbishop Borromeo is the human agent of the conversion of the Unnamed and the deliverer of multitudes of the poor and oppressed in the region of Milan during the plague.
Even though Manzoni clearly held the historical Borromeo and his fictional Fra Cristoforo in high regard, The Betrothed is able to present them as more than stock characters. One is not left with the impression of hagiography. I also found it interesting that, while the conversions of Cristoforo and the Unnamed were distinctively Catholic--nothing of the Reformed distinctives of the double imputation of sin and righteousness (or the Evangelical "personal relationship with Jesus")--they were not "sacramental." In other words, while Manzoni treats conversion in terms of internal repentance and subsequent virtuous activities, his accounts should not be off-putting to those who hold to justification by faith alone.
According to Attilio, every Italian teen spends a considerable portion of his or her sophomore year of high school studying The Betrothed. An edited version would do well for an AP class in an American high school. Treating it as only a romance would, however, do The Betrothed and Manzoni a disservice. It is a distinctively Christian novel whose themes of faith, repentance, and a life of dependent virtue (sanctification for us Protestants) are an integral part of the story.