UV and x-ray photoemission spectroscopy (PES) allows for the determination of the occupied electronic band structure of solids, whereas inverse photoemission spectroscopy (IPES) renders complementary information on the unoccupied electronic states. Both methods combined in situ can provide a precise information on the electronic band gap of semiconductors. In this work, Bayes' Maximum Entropy Method (MaxEnt) is applied to the deconvolution of PES and IPES spectra. To this effect, a dedicated algorithm has been developed and implemented. A non-uniform prior distribution and a simple misfit criterion for the regularization parameter are used. Likelihood errors are discussed. Minimization is based on a universal variable metric subroutine. MaxEnt provides a useful instrument to distinguish between physical and resolution effects especially when the spectrometer function varies with excitation energy, as is in particular the case for IPES. IPES is by principle resolution-limited due to the intrinsic divergence of the impinging low-energy electron beam. In the experimental section, the occupied and unoccupied electronic structure of the layered crystal hafnium disulfide is examined. Angle resolved PES and IPES measurements are discussed in the context of available electronic band structure calculations. The photoemission measurements have been carried out using synchrotron radiation at HASYLAB/DESY. (See also M.Traving, T.Seydel et al.; Physical Review B vol. 63, p. 035107 (2001).)