The catalyzed dissociation of molecular hydrogen on the surfaces of diverse materials is currently widely studied due to its importance in a broad range of hydrogenation reactions that convert noxious exhaust products and/or greenhouse gases into added-value greener products such as methanol. In the search for viable replacements for expensive late transition metal catalysts TiC has been increasingly investigated as a potential catalyst for H2 dissociation. Here, we report on a combination of experiments and density functional theory calculations on the well-defined TiC(001) surface revealing that multiple H and H2 species are available on this substrate, with different binding configurations and adsorption energies. Our calculations predict an initial occupancy of H atoms on surface C atom sites, which then enables the subsequent stabilization of H atoms on top of surface Ti atoms. Further H2 can be also molecularly adsorbed over Ti sites. These theoretical predictions are in full accordance with information extracted from X-ray photoemission spectroscopy and temperature-programmed desorption experiments. The experimental results show that at high coverages of hydrogen there is a reconstruction of the TiC(001) surface which facilitates the binding of the adsorbate.