Semiconductors with complex anisotropic morphologies in solar to chemical energy conversion devices enhance light absorption and overcome limiting charge transport in the solid. However, structuring the solid-liquid interface has also implications on concentration distributions and diffusive charge transport in the electrolyte. Quantifying the link between morphology and those multi-physical transport processes remains a challenge. Here we develop a coupled experimental-numerical approach to digitalize the photoelectrodes by high resolution FIB-SEM tomography, quantitatively characterize their morphologies and calculate multi-physical transport processes on the exact geometries. We demonstrate the extraction of the specific surface, shape, orientation and dimension of the building blocks and the multi-scale pore features from the digital model. Local current densities at the solid-liquid interface and ion concentration distributions in the electrolyte have been computed by direct pore-level simulations. We have identified morphology-dependent parameters to link the incident-light-to-charge-transfer-rate-conversion to the material bulk properties. In the case of a structured lanthanum titanium oxynitride photoelectrode (Eg = 2.1 eV), with an absorptance of 77%, morphology-induced mass transport performance limitations have been found for low bulk ion concentrations and diffusion coefficients.