Multi-component heterogeneous catalysts are among the top candidates for converting greenhouse gases into valuable compounds. Combinations of Cu, Zn, and ZrO2 (CZZ) have emerged as promisingly efficient catalysts for CO2 hydrogenation to methanol. To explore the catalytic mechanism, density functional theory (DFT) calculations and the energetic span model (ESM) were used to study CO2 conversion routes to methanol on CuZn-ZrO2 interfaces with a varying Zn content. Our results demonstrate that the presence of Zn sites at the interface improves CO2 binding. However, the adsorption and activation energies are insensitive to Zn concentration. The calculations also show that the hydrogenation of adsorbate oxygen atoms at the interface is kinetically more favourable and requires hydrogen spillover from the metal to the zirconia. This leads to barriers that are lower than those reported on interface or metal-only sites in previous literature. While DFT calculations alone are unable to identify which one of the competing pathways is more favourable, the ESM model predicts that the carboxyl pathway has a higher turnover frequency than the formate route. Our findings also show the importance of considering effects such as hydrogen spillover which take place at a metal-oxide interface when modelling complex catalytic environments.