Photoionization of the solar abundance diffuse ionized media (DIM) in NGC 1068 by anisotropic nuclear emission is studied. It is shown that the emission characteristics can be understood in the light of the developing picture of the galaxy in which its intrinsic type 1 Seyfert nucleus, concealed by an obscuring medium, is visible only through scattered, polarized light. The gas excitation is anisotropic, the high-excitation gas along the jet axis being photoionized by direct nuclear continuum, while the lower excitation gas away from the axis sees only indirect nuclear emission scattered into it. A model of low optical depth, near-nuclear Thomson scattering is considered in detail, and it is shown that, even with moderate dust extinction, this mechanism is sufficient to energize the DIM. 56 refs.