ABSTRACT We develop a hybrid model of galactic chemical evolution that combines a multiring computation of chemical enrichment with a prescription for stellar migration and the vertical distribution of stellar populations informed by a cosmological hydrodynamic disc galaxy simulation. Our fiducial model adopts empirically motivated forms of the star formation law and star formation history, with a gradient in outflow mass loading tuned to reproduce the observed metallicity gradient. With this approach, the model reproduces many of the striking qualitative features of the Milky Way disc’s abundance structure: (i) the dependence of the O/Fe–Fe/H distribution on radius Rgal and mid-plane distance |z|; (ii) the changing shapes of the O/H and Fe/H distributions with Rgal and |z|; (iii) a broad distribution of O/Fe at sub-solar metallicity and changes in the O/Fe distribution with Rgal, |z|, and Fe/H; (iv) a tight correlation between O/Fe and stellar age for O/Fe > 0.1; (v) a population of young and intermediate-age α-enhanced stars caused by migration-induced variability in the Type Ia supernova rate; (vi) non-monotonic age–O/H and age–Fe/H relations, with large scatter and a median age of ∼4 Gyr near solar metallicity. Observationally motivated models with an enhanced star formation rate ∼2 Gyr ago improve agreement with the observed age–Fe/H and age–O/H relations, but worsen agreement with the observed age–O/Fe relation. None of our models predict an O/Fe distribution with the distinct bimodality seen in the observations, suggesting that more dramatic evolutionary pathways are required. All code and tables used for our models are publicly available through the Versatile Integrator for Chemical Evolution (VICE; https://pypi.org/project/vice).