Holes in metal films do not allow the propagation of light if the wavelength is much larger than the hole diameter, establishing such nanopores as so-called zero-mode waveguides (ZMWs). Molecules, on the other hand, can still pass through these holes. We use this to detect individual fluorophore-labelled molecules as they travel through a ZMW and thereby traverse from the dark region to the illuminated side, upon which they emit fluorescent light. This is beneficial both for background suppression and to prevent premature bleaching. We use palladium as a novel metal-film material for ZMWs, which is advantageous compared to conventionally used metals. We demonstrate that it is possible to simultaneously detect translocations of individual free fluorophores of different colours. Labelled DNA and protein biomolecules can also be detected at the single-molecule level with a high signal-to-noise ratio and at high bandwidth, which opens the door to a variety of single-molecule biophysics studies.