A model for two-component coadsorption is introduced and used to study the structure of the phases which occur at low temperature during the underpotential deposition of copper on the (111) surface of gold in the presence of bisulfate ions. The structure,of the voltage dependent ground state configurations is rigorously obtained, and the Pirogov-Sinai theory is used to prove the existence of low-temperature phases in the model which are similar in structure to the ground state configurations. The sequence and structure of the low-temperature phases which occur in the model as the voltage is changed are essentially the same as those obtained experimentally at ambient temperatures during the underpotential deposition process.