We investigate the atomic (H i) and molecular (H2) Hydrogen content of normal galaxies by combining observational studies linking galaxy stellar and gas budgets to their host dark matter (DM) properties, with a physically grounded galaxy formation model. This enables us to analyse empirical relationships between the virial, stellar and gaseous masses of galaxies, and explore their physical origins. Utilizing a semi-analytic model (SAM) to study the evolution of baryonic material within evolving DM haloes, we study the effects of baryonic infall and various star formation and feedback mechanisms on the properties of formed galaxies using the most up-to-date physical recipes. We find that in order to significantly improve the agreement with observations of low-mass galaxies, we must suppress the infall of baryonic material and exploit a two-phase interstellar medium, where the ratio of H i to H2 is determined by the galactic disc structure. Modifying the standard Schmidt–Kennicutt star formation law, which acts upon the total cold gas in galaxy discs and includes a critical density threshold, and employing a star formation law which correlates with the H2 gas mass results in a lower overall star formation rate. This, in turn, allows us to simultaneously reproduce stellar, H i and H2 mass functions of normal galaxies.