Equations of motion are presented that describe the kinetics of phase separation of mixtures of rods and coils into an isotropic phase rich in coils and a nematic phase rich in rods. The equations were derived using dynamical mean field theory and contain only a few pure-component parameters, such as the self-diffusion coefficients and molecular weights of the rods and coils. In such a system, both composition and orientation density evolve with time in a coupled fashion, so the presence of orientational order has a pronounced effect on the domain morphology at all but the latest stages of phase separation. The formalism presented here will provide insights into the control of domain morphology and properties of bicontinuous polymeric structures produced by quenching spinodal decomposition processes.