A new model for the source distribution of galactic soft X-ray (B and C band) emission is presented. From the mean dependence of count rates on galactic latitudeb (i.e., the brightness distribution), we derive the soft X-ray source functionQ as function of the optical depth τ by solving the equation of radiative transfer with the aid of a Laplace transform. Contrary to older ‘Heaviside’ step models,Q is found to increase strongly, but not abruptly, in the range 1.5<τ<2.5, indicating a noticeable emission of X-rays from beyond theHi scale height. Using standard X-ray absorption cross-sections for the interstellar medium, we find that the B band X-ray emission coefficient is non-zero within theHi disk and has a maximum at az-value slightly above the Hi scale height. In the C band, the emission coefficient slightly decreases with increasingz, at least up to theHi scale height. A non-zero source function near the galactic plane implies that the interstellar medium (ISM) within theHi scale height is not only an absorbing layer but is mixed with X-ray emitting regions. The so-called ‘local hot bubble’ is adopted as one of these regions. The maximum of the B band emission coefficient, together with the sharp increase ofQ, is strong evidence for the existence of a galactic soft X-ray ‘halo’, and, moreover, give rise to the assumption of a general intergalactic X-ray background. The ‘effective’ absorption cross-sections σ given in the literature, based on an (pure) exponential dependence in the negative correlation between count rates andHi column densities, were biased to be too small, in particular in the B band. In replacing the Heaviside step (in the ISM) by a smoothed transition region, these inconsistencies become spurious.