The influence of mixing on the curvature free energy of a thermodynamically open, reversibly formed vesicle bilayer is investigated by deriving expressions for the various contributions to the Mayer bending constant k(bi) as functions of the structure of aggregated surfactants as well as the solution state (electrolyte concentration, average composition in the bilayers, etc). k(bi) is shown to be lowered in surfactant mixtures as a result of the fact that a mixed vesicle bilayer that is open in the thermodynamic sense may assume different compositions in the inner and outer monolayers. The net contribution of all terms related to surfactant mixing is to lower k(bi). The magnitude of this reduction increases with increasing asymmetry between the two surfactants with respect to charge number, head group size, and tail length. The reduction of k(bi) due to mixing is most pronounced for mixtures where the surfactant that carries charge or has the highest charge number has the larger head group and the smaller tail.