Molybdenum carbides are increasingly used in heterogeneously catalyzed hydrogenation reactions, which imply the adsorption and dissociation of molecular hydrogen. Here a systematic density functional theory based study, including or excluding dispersion terms, concerning the interaction and stability of H2 with cubic δ-MoC(001) and orthorhombic β-Mo2C(001) surfaces is presented. In the latter case the two possible C or Mo terminations are considered. In addition, different situations for the H covered surfaces are examined. Computational results including dispersive forces predict as essentially spontaneous dissociation of H2 on β-Mo2C(001) independently of the surface termination, whereas on δ-MoC(001) molecular hydrogen dissociation implies a small but noticeable energy barrier. Furthermore, the ab initio thermodynamics formalism has been used to compare the stability of different H coverages. Finally, core level binding energies and vibrational frequencies are presented with the aim to assist the interpretation of yet unavailable data from X-ray photoelectron and infrared spectroscopies.