The prototypical correlated metal Sr_{2}RhO_{4} was studied using optical and photoemission spectroscopy. At low energies and temperatures, the optical data reveal a complex, multicomponent response that on the surface points to an unconventional metallic state in this material. Via a comparison with photoemission, the anomalous optical response may be attributed to an unexpectedly strong interband transition near 180 meV between spin-orbit coupled bands that are nearly parallel along ΓX. This spin-orbit coupling effect is shown to occur in a number of related metallic ruthenates and explains the previously puzzling optical properties reported for these materials.