The biconical radiation pattern extending from an active galactic nucleus (AGN) may strongly photoionize the circumnuclear interstellar medium (ISM) and stimulate emission from the narrow-line region (NLR). Observations of the NLR may provide clues to the structure of dense material that preferentially obscures the bicone at certain angles, and may reveal the presence of processes in the ISM tied to AGN accretion and feedback. Ground-based integral field units may study these processes via well-understood forbidden diagnostic lines such as [O III] and [S II], but scales of ~tens of parsecs remain challenging to spatially resolve at these wavelengths for all but the nearest AGN. We present recent narrow-filter Hubble Space Telescope observations of diagnostic forbidden ([O III], [S II]) and Balmer (Hα, Hβ) lines in the NLR of IC 5063. This AGN's jet inclination into the plane of the galaxy provides an important laboratory for strong AGN-host interactions. We find evidence for a low-ionization loop which emits brightly in [S II] and [N II], and which may arise from plume-like hot outflows that ablate ISM from the galactic plane before escaping laterally. We also present spatially resolved Baldwin-Phillips-Terlevich diagnostic maps of the IC 5063 NLR. These maps suggest a sharp transition to lower-ionization states outside the jet path, and that such emission is dominated by ~10-40 pc clumps and filamentary structure at large (≫25°) angles from the bicone axis. Such emission may arise from precursorless shocks when AGN outflows impact low-density hot plasma in the cross cone. * Based on observations made with the NASA/ESA Hubble Space Telescope, obtained from the data archive at the Space Telescope Science Institute. STScI is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555. These observations are associated with programs #8598 and #15609.