The soft X-ray background in the 0.1-1.0 keV band is known to be produced by at least three sources; the Local Hot Bubble (LHB), the extragalactic power law (EPL), and a seemingly galactic component that lies outside the bulk of the absorption that is due to the ISM of the galactic disk. This last component, which we call the Trans-Absorption Emission (TAE), has been modeled by a number of groups who have derived disparate measures of its temperature. The differences have arisen from differing assumptions about the structure of the emitting gas and unrecognized methodological difficulties. In particular, spectral fitting methods do not uniquely separate the TAE from the foreground emission that is due the LHB. This ''degeneracy'' can be resolved using the angular variation of the absorption of the TAE. We show that the TAE cannot be characterized by a single thermal component; no single-component model can be consistent with both the spectral energy distribution of the TAE emission and the angular variation due to absorption by the galactic disk. We use the angular anticorrelation of the ROSAT All-Sky Survey with the galactic absorption to separate local from distant emission components, and to fit the spectral energy distribution of the resulting distant emission. We find that the emission is best described by a two-thermal-component model with logT(sub S) = 6.06(sup 0.14, sub -0.12) and log T(sub H) = 6.42(sup 0.14, sub -0.12). This two-thermal-component TAE fits the ROSAT spectral energy distribution significantly better than single-component models, and is consistent with both angular variation and spectral constraints.