The performance of photosensitizers in the field of, for example, solar energy conversion, relies on their light‐harvesting efficiency in the visible region, population of long‐lived charge‐separated intermediates, as well as their charge‐accumulation capacity amongst other properties. In this computational study, we investigate the photophysical properties of a bis(bipyridyl)ruthenium(II)‐based black dye (Ru) incorporating a chromophoric unit based on a thiazole donor‐acceptor push‐pull motif. The combination of two light‐harvesting units, that is, the Ru(II)polypyridyl and the thiazole‐based organic dye, yields close‐lying metal‐to‐ligand charge transfer (MLCT) states, involving both ligand spheres as well as intra‐ligand charge transfer (ILCT) states of the organic dye. Due to the combination of inorganic and organic chromophores the computational modelling of the photophysics of Ru is challenging. To this aim, time‐dependent density functional theory and multiconfigurational methods are applied. The excited‐state properties obtained for the states of interest are rationalized by electronic absorption and resonance Raman spectroscopies. The CAM‐B3LYP functional was found to accurately describe the ground‐ and excited‐state properties of Ru. Finally, excited‐state relaxation pathways and the multi‐charge‐accumulation capacity were addressed. Despite the unidirectional nature of the MLCTthia and ILCTthia transitions, the thiazole unit is merely capable to store one redox equivalent.