Analytical results for the structure factor of a two-component model plasma that describe an electron-ion plasma with modified interaction are derived from a Green function approach in different approximations. The random-phase approximation is improved by including the dynamic collision frequency, and results for the long-wavelength limit are extended to arbitrary wave numbers using the Mermin ansatz. After taking the classical limit of the resulting expressions, they are compared with molecular dynamics simulation results for the classical two-component model plasma.