We examine the balance of surface bonding and hydrogen bonding in the mixed OH + H2O overlayer on Pt(111), Cu(111), and Cu(110) via density functional theory calculations. We find that there is a cooperativity effect between surface bonding and hydrogen bonding that underlies the stability of the mixed phase at metal surfaces. The surface bonding can be considered to be similar to accepting a hydrogen bond, and we can thereby apply general cooperativity rules developed for hydrogen-bonded systems. This provides a simple understanding of why water molecules become more strongly bonded to the surface upon hydrogen bonding to OH and why the OH surface bonding is instead weakened through hydrogen bonding to water. We extend the application of this simple model to other observed cooperativity effects for pure water adsorption systems and H3O+ on metal surfaces.