The Far-Infrared Absolute Spectrophotometer (FIRAS) on the COBE satellite has conducted an unbiased survey of the far-infrared emission from our Galaxy. The first results of this survey were reported by Wright et al. (1991). We report the results of new analyses of this spectral survey, which includes emission lines from 158 mum C+, 122 and 205 mum N+, 370 and 609 mum C0, and CO J = 2-1 through J = 5-4. We report the morphological distribution along the Galactic plane (b = 0-degree) of the spectral line emission, and the high Galactic latitude intensities of the C+ and 205 mum N+ emission. In the Galactic plane the 205 mum line of N+ generally follows the 158 mum C+ line distribution, but the intensities scale as I(N+ 205 mum) infinity I(C+ 158 mum)1.5 toward the inner Galaxy. The high Galactic latitude intensity of the 158 mum fine-structure transition from C+ is I(C+ 158 mum) = (1.43 +/- 0.12) x 10(-6) csc \b\ ergs cm-2 s-1 sr-1 for \b\ > 15-degrees, and it decreases more rapidly than the far-infrared intensity with increasing Galactic latitude. C+ and neutral atomic hydrogen emission are closely correlated with a C+ cooling rate of (2.65 +/- 0.15) x 10(-26) ergs s-1 (H atom)-1. We conclude that this emission arises almost entirely from the cold neutral medium. The high Galactic latitude intensity of the 205 mum fine-structure transition from N+ is I(N+ 205 mum) = (4 +/- 1) x 10(-8) csc \b\ ergs cm-2 s-1 sr-1 arising entirely from the warm ionized medium. We estimate the total ionizing photon rate in the Galaxy to be phi = 3.5 x 10(53) ionizing photons per second, based on the 205 mum N+ transition.