Evolutionary searches have predicted a number of ternary Ca-S-H phases that could be synthesized at pressures of 100-300 GPa. P63/mmc CaSH2, Pnma CaSH2, Cmc21 CaSH6, and I4̅ CaSH20 were composed of a Ca-S lattice along with H2 molecules coordinated in a "side-on" fashion to Ca. The H-H bond lengths in these semiconducting phases were elongated because of H2 σ → Ca d donation, and Ca d → H2 σ* back-donation, via a Kubas-like mechanism. P6̅m2 CaSH3, consisting of two-dimensional HS and CaH2 sheets, was metastable and metallic above 128 GPa. The presence of van Hove singularities increased its density of states at the Fermi level and concomitantly the superconducting critical temperature, which was estimated to be as high as ∼100 K at 128 GPa. This work will inspire the search for superconductivity in materials based upon honeycomb HX (X = S, Se, Te) and MH2 (M = Mg, Ca, Sr, Ba) layers under pressure.