We report an approach for extracting the optical constants of bimetallic Ag-Au nanoparticles from the measured surface-plasmon (SP) extinction spectra. The dielectric function of the metal is expressed as an analytic function of the wavelength in which the interband (and all other non-Drude) contributions to the dielectric function are represented by a sum of Lorentz functions. This expression is then used to fit the experimental extinction spectra to appropriate functions based on Mie theory. Three Lorentz functions (plus a Drude term) were found to be sufficient to reproduce the dielectric functions of Ag and Au [P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972)] over the entire 0.6-6.5 eV range reported. With functions of this type, an excellent multiparameter fit of the measured extinction spectrum of colloidal Ag was obtained. Extinction spectra of a series of (Ag)Au hydrosols, prepared by reducing a gold precursor in the presence of previously synthesized silver seed particles with Au mole fractions ranging from 0.1 to 0.8, were measured. The extinction spectra show a single band (attributed to the surface plasmon) for all of the colloids produced, suggesting alloy formation. Transmission electron microscopy (TEM) images, however, indicate clear core-shell contrast for nanoparticles with Au mole fractions 0.4 and higher. With a presumed particle structure consisting of Ag core and Ag/Au alloy shell, very good fits were obtained for all of the measured extinction spectra by using a fitting strategy that restricted the number of parameters allowed to vary freely in the aforementioned dielectric function. The values of the dielectric function of the presumed shells were extracted in this manner as a function of wavelength. For particles with Au mole fraction 0.1-0.3, the results suggest an incompletely formed shell. For particles with higher Au mole fractions, the dielectric function of the shell gradually approaches that of Au. Overall, the results are consistent with a particle structure that consists of a Ag-rich core and Ag/Au alloy shell whose composition is gradually enriched in Au with increasing overall Au mole fraction. The dielectric function of the alloy shells cannot be written merely as a weighted average of the corresponding dielectric functions of Ag and Au. An almost linear decrease of the electron scattering rate in the particle's shell with the increasing Au mole fraction was determined through this fitting analysis. This was ascribed both to the confinement of the electrons within the shell (which increases in thickness with increasing Au mole fraction) and the gradual change of the composition, and, consequently, of the electrical conductivity of the shell.