Family Drama, Literary Fiction
While the genre of Howards End can certainly be said to be a family drama on a small scale – as in, it's about two very different families, the Wilcoxes and the Schlegels, and their difficulty reconciling with each other – we might also try and expand this term a little bit. The novel is both about the individual and the universal; while at first glance, the plot revolves around the relatively small and inconsequential lives of the very few characters we meet, its philosophical stakes are a lot higher. We might get a little loosey-goosey and say that this novel is also a drama of the human family and the need for sympathetic understanding.
On a less vague but still ambitious level, we could also say that it's specifically about the English part of that family tree; the novel is usually referred to as a "condition of England" novel, a genre in itself, in which an author approaches the question of the nation, attempting to figure out what makes England English, and if it can be improved upon – socially, politically, morally. Other famous "condition of England" novels you might have heard of include several of the works of Charles Dickens, especially Oliver Twist and Hard Times, and the novels of Elizabeth Gaskell, like North and South.
This gets us into the second genre we've chosen, literary fiction. This explicit project for the novel definitely means there's more at stake here than plot; this novel seriously works on so many levels, not all of them simple or straightforward.