A method to describe the quantum dynamics of photoinduced heterogeneous electron-transfer processes at dye-semiconductor interfaces is proposed. The method is based on a model Hamiltonian, the parameters of which are determined by first-principles electronic structure calculations and a partitioning scheme to define localized donor and acceptor states as well as donor-acceptor coupling matrix elements. On the basis of this modeling procedure, accurate quantum dynamical simulations are performed employing the multilayer multiconfiguration time-dependent Hartree method. As a representative example, applications to coumarin 343 adsorbed on titanium oxide nanoparticles are presented. The results of the simulations show that the ultrafast electron-injection process in this system is accompanied by electronic coherence effects, which are partially quenched due to electronic-nuclear coupling.