Considering the significance of hexagonal copper thiocyanate (β-CuSCN) in several optoelectronic technologies and applications, it is essential to investigate its electronic structure and surface properties. Herein, we have employed density functional theory (DFT) calculations to characterise the band structure, density of states, and the energy-dependent X-ray photoelectron (XPS) valence band spectra at variable excitation energies of β-CuSCN. The surface properties in the absence and presence of dimethyl sulfoxide (DMSO), a solvent additive for improving perovskite solar cells’ power conversion efficiency, have also been systematically characterised. β-CuSCN is shown to be an indirect band gap material (Eg = 3.68 eV) with the valence band edge demonstrated to change from being dominated by Cu-3d at soft X-ray ionisation photon energies to Cu-3p at hard X-ray ionisation photon energies. The adsorption energy of dimethyl sulfoxide (DMSO) on the (100) and (110) β-CuSCN surfaces is calculated at −1.12 and −0.91 eV, respectively. The presence of DMSO on the surface is shown to have a stabilisation effect, lowering the surface energy and tuning the work function of the β-CuSCN surfaces, which is desirable for organic solar cells to achieve high power conversion efficiencies.