Literary Fiction, Historical Fiction
Middlemarch falls into the category of literary fiction pretty tidily: it's a novel, it's written in prose, and the third-person narrator is concerned with developing characters that have psychological depth and that react to events in a way that seems both realistic and sympathetic (i.e., we're able to imagine ourselves in their position, even if we don't agree with it).
Calling Middlemarch a work of "historical fiction" is slightly more problematic. What makes something "historic," anyway? Middlemarch was written in 1870-71, but it takes place in 1830-32. Does a gap of forty years make it historical fiction? The novelist who (arguably) invented historical fiction, Sir Walter Scott, wrote his first novel, Waverley, about historical events that took place sixty years before the time of writing. So, if sixty years makes something "historical fiction," why not forty years?