The understanding of the fundamental physical properties of metal-organic and organic-organic interfaces is crucial for improving the performance of organic electronic devices. This is particularly true for (multilayer) systems containing several molecular species due to their relevance for donor-acceptor systems. A prototypical heteromolecular bilayer system is copper-II-phthalocyanine (CuPc) on 3,4,9,10-perylene-tetra-carboxylicdianhydride (PTCDA) on Ag(111). In an earlier work we have reported a commensurate registry between both organic layers and an enhanced charge transfer from the Ag substrate into the organic bilayer film [Phys. Rev. Lett. 108, 106103 (2012)], which both indicate an unexpectedly strong intermolecular interaction across the organic-organic interface. Here we present new details regarding electronic and geometric structure for the same system. In particular, we provide evidence that the enhanced charge transfer from the substrate into the organic bilayer does not involve CuPc electronic states, hence, there is no significant charge transfer into the second organic layer. Furthermore, we report vertical bonding distances revealing a shortening of the PTCDA-Ag(111) distance upon CuPc adsorption. Thus, electronic and geometric properties (charge transfer and bonding distance, respectively) both indicate a strengthening of the PTCDA-Ag(111) bond upon CuPc adsorption. We explain these findings-in particular the correlation between CuPc adsorption and increased charge transfer into PTCDA-in a model involving an intermolecular screening mechanism.