Abstract We present an analysis of the relationship between the CO–H2 conversion factor (αCO) and total mass surface density (Σtot) in star-forming galaxies at z < 1.5. Our sample, which is drawn from the IRAM Plateau de Bure HIgh-z Blue Sequence Survey (PHIBSS) and the CO Legacy Database for GASS (COLD GASS), includes ‘normal’, massive star-forming galaxies that dominate the evolution of the cosmic star formation rate (SFR) at this epoch and probe the Σtot regime where the strongest variation in αCO is observed. We constrain αCO via existing CO observations, measurements of the SFR and an assumed molecular gas depletion time (tdep = Mgas/SFR) – the latter two of which establish the total molecular gas mass independent of the observed CO luminosity. For a broad range of adopted depletion times, we find that αCO is independent of total mass surface density, with little deviation from the canonical Milky Way value. This runs contrary to a scenario in which αCO decreases as surface density increases within the extended clouds of molecular gas that potentially fuel clumps of star formation in z ∼ 1 galaxies, similar to those observed in local ultra-luminous infrared galaxies. Instead, our results suggest that molecular gas, at both z ∼ 0 and z ∼ 1, is primarily in the form of self-gravitating molecular clouds. While CO observations suggest a factor of ∼3 reduction in the average molecular gas depletion time between z ∼ 0 and z ∼ 1, we find that, for typical galaxies, the structure of molecular gas and the process of star formation at z ∼ 1 is otherwise remarkably similar to that observed in local star-forming systems.