Heterojunctions between p-type cuprous oxide (Cu2O) and suitable n-type layers stand out as some of the best performing and abundant oxide photoabsorbers currently available for the generation of hydrogen with photoelectrochemical cells or conversion of solar energy to electricity. In this contribution, we used drift-diffusion semiconductor modeling to investigate the mechanism governing the charge transport in TiO2/Ga2O3/Cu2O and TiO2/Al:ZnO/Cu2O heterojunctions. The simulated photovoltage 0.9 V for TiO2/Ga2O3/Cu2O agrees well with the measured value of 1.0 V and the governing mechanism is identified to be thermionic emission of electrons across the Ga2O3/TiO2 interface. By modeling an optimized increase in Ga2O3 donor concentration, a photovoltage improvement of only 0.1 V is achievable, whereas further optimizing the electron affinity of Ga2O3 may lead to more significant improvement approaching 0.7 V. The optimized electron affinity of Ga2O3 enabled a simulated photovoltage of 1.6 V, close to the theoretical limit for Cu2O with a 2.17 eV bandgap energy. Additionally, we find that simulations can reproduce the measured photovoltage of TiO2/Al:ZnO/Cu2O only when an interface recombination layer at the Al:ZnO/Cu2O interface is included in the model. Our findings enable detailed understanding of the charge transport mechanism in Cu2O heterojunctions and offer various design directions for further photovoltage improvement.