The adsorption of molecular hydrogen (H2) in the alkali-graphite intercalate KC24 has been studied using simultaneous neutron diffraction and Compton scattering. Neutron Compton scattering data for the (H2)xKC24 system (x = 0-2.5) were measured at T = 1.5 K as a function of the relative orientation between the neutron beam and the intercalate c-axis. Synchronous with the above proton-recoil measurements, high-resolution diffraction patterns were measured in backscattering geometry. From these diffraction measurements, the intrinsic mosaicity of the Papyex-based intercalate was determined to be approximately 15 degrees half-width-at-half-maximum, in good agreement with previous studies [Finkelstein et al., Physica B, 2000, 291, 213]. Hydrogen uptake by the intercalate leads to a distinct and readily detectable broadening of the isotropic Compton profile compared to bulk H2, indicative of an enhanced interaction of the H2 molecule with the surrounding solid-state environment. Total proton-recoil intensities also scale linearly with the amount of adsorbed hydrogen. Taking as our starting point previous experimental and theoretical results, the isotropic widths of the proton momentum distributions can be explained on the basis of three energy scales, namely, intramolecular H-H vibrations, followed by H-H librations and H2 centre-of-mass translations. From the coverage dependence of these neutron data, we also establish an upper bound of approximately 10 meV for intermolecular hydrogen-hydrogen interactions. Finally, we observe a weak anisotropy of the width of the proton momentum distributions. Comparison of these experimental data with first-principles predictions indicates that subtle quantum mechanical effects associated with particle delocalisation and exchange lie at the heart of the observed behaviour. Overall, these results demonstrate the suitability and largely untapped potential of neutron Compton scattering to explore H2 uptake by solid-state hosts.