Spectrophotometric observations with the Hawaii Imaging Fabry-Perot Interferometer (HIFI) of the H-alpha and [N II] lambda-lambda-6548, 6584 lines has detected a diffuse ionized medium (DIM) pervading the inner approximately 10 kpc diameter disk of the nearby, luminous Seyfert galaxy NGC 1068. The physics and dynamics of this energetic gas are distinct from the population of adjacent disk H II regions which have line intensity ratios [N II] lambda-6584/H-alpha < 0.5, equivalent widths of H-alpha almost-equal-to 15-100 angstrom, and [N II] lambda-6584 line widths approximately 100 km s-1 FWHM. The DIM exhibits broader lines (150-250 km s-1 FWHM) than the H II regions which suggests an exponential scale height of at least approximately 400 pc, compared with approximately 50 pc for the cold neutral phase. The DIM is characterized by strong [N II] lambda-6584 emission (3.0 x 10(41) ergs s-1) when compared to H-alpha (1.2 x 10(41) ergs s-1), with [N II] lambda-6584/H-alpha approximately 1 throughout and reaching 2-3 NE and SW along the radio axis. Because the chemical abundances throughout the inner disk are known to be approximately solar and we have corrected for Balmer absorption by the underlying stellar population, the extent of the high [N II] lambda-6584/H-alpha gas and, for a filling factor pie, the associated cooling time (almost-equal-to 2 x 10(5)pie-0.5 yr) indicate substantial excitation of the DIM. We discuss heating by the Seyfert nucleus and the extended starburst region because these regions share the bolometric luminosity.