We present estimations of the shear viscosity of a hydrogen-carbon mixture at various concentrations computed by molecular dynamics in the frame of Kubo currents obtained directly at the hydrodynamic limit through the Bernu-Vieillefosse formalism (Bernu B. and Vieillefosse P., Phys. Rev. A, 18 (1978) 2345). It is shown that, depending on the initial temperature of the mixture, a small amount of carbon in the hydrogen plasma can strongly reduce the viscosity (kinetic regime), but in some cases the mixing can lead to an increase (strong coupling). Those results are fitted and extended to an arbitrary mixture with the help of a one-fluid model.