Simultaneous Chandra X-ray and Hubble Space Telescope FUV observations of Jupiter's aurorae carried out in February 2003 have been re-examined to investigate the spatial morphology of the X-ray events in different energy bands. The data clearly show that in the Northern auroral region (in the main auroral oval and the polar cap) events with energy > 2 keV are located at the periphery of those with energy < 2 keV and coincide with FUV bright features. In addition, X-ray spectra extracted from the areas where the two event distributions are concentrated possess different shapes. We associate the > 2 keV events (∼45 MW emitted power) with the electron bremsstrahlung component recently revealed by XMM-Newton in the spectra of Jupiter's aurorae, and the < 2 keV emission (∼230 MW) with the product of ion charge exchange, now established as the likely mechanism responsible for the soft X-ray Jovian aurora. We suggest that the same population of energetic electrons may be responsible for both, the X-ray bremsstrahlung and the FUV emission of Jupiter's aurorae. Comparison of the > 2 keV X-ray and FUV (340 GW) powers measured during the observations shows that they are broadly consistent with the predicted emissions from a population of energetic electrons precipitating in the planet's atmosphere, thus supporting our interpretation.