Aperture photometry from our own observations and the literature is presented for the 12 mu m galaxies in the near-infrared J, H, and K bands and, in some cases, in the L band. These data are corrected to ''total'' near-infrared magnitudes (with a typical uncertainty of 0.3 mag) for a direct comparison with our IRAS fluxes which apply to the entire galaxy. The corrected data are used to derive integrated total near-infrared and far-infrared luminosities. We then combine these with blue photometry and an estimate of the flux contribution from cold dust at wavelengths longward of 100 mu m to derive the first bolometric luminosities for a large sample of galaxies. The presence of nonstellar radiation at 2-3 mu m correlates very well with nonstellar IRAS colors. This enables us to identify a universal Seyfert nuclear continuum from near- to far-infrared wavelengths. Thus, there is a sequence of infrared colors which runs from a pure ''normal galaxy'' to a pure Seyfert/quasar nucleus. Seyfert 2 galaxies fall close to this same sequence, although only a few extreme narrow-line Seyfert galaxies have quasar-like colors, and these show strong evidence of harboring an obscured broad-line region. A corollary is that the host galaxies of Seyfert nuclei have normal near- to far-infrared spectra on average. Starburst galaxies lie significantly off the sequence, having a relative excess of 60 mu m emission probably as a result of stochastically heated dust grains. We use these correlations to identify several combinations of infrared colors which discriminate between Seyfert 1 and 2 galaxies, LINERs, and ultraluminous starbursts. In the infrared, Seyfert 2 galaxies are much more like Seyfert Is than they are like starbursts, presumably because both kinds of Seyferts are heated by a single central source, rather than a distributed region of star formation. Moreover, combining the [25-2.2 mu m] color with the [60-12 mu m] color, it appears that Seyfert 1 galaxies are segregated from Seyfert 2 galaxies and starburst galaxies in a well-defined region characterized by the hottest colors, corresponding to the flattest spectral slopes. Virtually no Seyfert 2 galaxy is present in such a region. To reconcile this with the ''unified scheme'' for Seyfert 1 and 2 galaxies would therefore require that the higher frequency radiation from the nuclei of Seyfert 2 galaxies to be absorbed by intervening dust and reemitted at lower frequencies. We find that bolometric luminosity is most closely proportional to 12 mu m luminosity. The 60 and 25 mu m luminosities rise faster than linearly with bolometric luminosity, while the optical flux rises less than linearly with bolometric luminosity. This result is a confirmation of the observation that more luminous disk galaxies have relatively more dust-enshrouded stars. Increases in the dust content shifts luminosity from the optical to 25-60 mu m, while leaving a ''pivot point'' in the mid-IR essentially unchanged. Thus, 12 mu m selection is the closest available approximation to selection by a limiting bolometric flux, which is approximately 14 times nu L(nu) at 12 mu m for non-Seyfert galaxies. It follows that future deep surveys in the mid-infrared, at wavelengths of 8-12 mu m, will simultaneously provide complete samples to different bolometric flux levels of normal and active galaxies, which will not suffer the strong selection effects present both in the optical-UV and far-infrared.
