here) which mainly listed the various genres to which any given Batman story might belong. Seeing from the stats that this post had been viewed, I reread it and then expanded it a bit with a few examples. I think that this is a significant point.
Most series in popular fiction belong to a single genre. Sherlock Holmes, who is just one of the Batman's many precursors, is exclusively a Detective. Doyle wrote about the supernatural but kept it out of his Holmes series. Holmes investigated an apparent vampire case with emphasis on the "apparent." A recent Holmes film preserved its status as a detective story right at the end when Holmes proved that the supernatural events had been faked.
Wayne can solve mysteries and fight vampires as well as alien invaders and can do this alone or in alliance with superheroes. Another composite format is the X Files TV series where any episode can be fantasy, sf or mystery but the Batman's range is broader. The greatest contrast is between the Adam Ward TV series and Frank Miller's The Dark Knight mini-series, collected as The Dark Knight Returns. The cover of Miller's Batman Year One Part 1 (see image) also displays a serious treatment of the character's origin and motivation.