Mo2C catalysts are widely used in hydrogenation reactions; however, the role of the C and Mo terminations in these catalysts is not clear. Understanding the binding of adsorbates is key for explaining the activity of Mo2C. The adsorption of acetylene and ethylene, probe molecules representing alkynes and olefins, respectively, was studied on a β-Mo2C(100) surface with C and Mo terminations using calculations based on periodic density functional theory. Moreover, the role of the C/Mo molar ratio was investigated to compare the catalytic potential of cubic (δ-MoC) and orthorhombic (β-Mo2C) surfaces. The geometry and electronic properties of the clean δ-MoC(001) and β-Mo2C(100) surfaces have a strong influence on the binding of unsaturated hydrocarbons. The adsorption of ethylene is weaker than that of acetylene on the surfaces of the cubic and orthorhombic systems; adsorption of the hydrocarbons was stronger on β-Mo2C(100) than on δ-MoC(001). The C termination in β-Mo2C(100) actively participates in both acetylene and ethylene adsorption and is not merely a spectator. The results of this work suggest that the β-Mo2C(100)-C surface could be the one responsible for the catalytic activity during the hydrogenation of unsaturated C≡C and C═C bonds, while the Mo-terminated surface could be poisoned or transformed by the strong adsorption of C and CHx fragments.