Oxygen adsorbates are unavoidable on Cu in an aqueous environment. In this work, such a polycrystalline Cu surface is decorated with electrodeposited Cd. Optical second harmonic generation is used to probe the time resolved kinetics of co-adsorbed oxygen and Cd on this electrode. The optical data contain contributions from the linear dielectric functions, and second order susceptibility elements of the electrochemical interface. A phenomenological theory is presented to resolve the contributions of these optical parameters in the optical signal of the Cu surface. Electronic effects of the co-deposited oxygen and Cd on Cu are analyzed by testing the coverage dependent features of the interfacial optical parameters. Numerical calculations are performed for this analysis. The results are characterized in terms of a Cd-induced lowering of the surface work function of Cu. The results also demonstrate how second harmonic generation can be used to analyze the relatively complicated electrochemistry of Cu.