The hydromagnetic Rankine-Hugoniot relations are extended to allow for separate ion and electron temperatures and arbitrary degrees of freedom for ion and electron heating; when the degrees of freedom are unequal, this comprises an unclosed set of equations. The system is reduced to one equation in two unknowns containing the usual one-fluid model as a special case. Closure is achieved by means of empirical arguments for both subcritical and large Mach number shocks, and a general parametric solution is also presented. Analytic expressions for the fluid and field jumps are obtained and compared with various experimental observations.