We present a study of the resolved emission-line regions and an inner dust/gas disk in the Seyfert 2 galaxy Mrk 3, based on Hubble Space Telescope observations. We show that the extended narrow-line region (ENLR), spanning ~4 kpc, is defined by the intersection of the ionizing bicone of radiation from the AGN and the inner disk, which is not coplanar with the large-scale stellar disk. This intersection leads to different position and opening angles of the ENLR compared to the narrow-line region (NLR). A number of emission-line arcs in the ENLR appear to be continuations of dust lanes in the disk, supporting this geometry. The NLR, which consists of outflowing emission-line knots spanning the central ~650 pc, is in the shape of a backwards S. This shape may arise from rotation of the gas, or it may trace the original fueling flow close to the nucleus that was ionized after the AGN turned on.