We introduce a kinetic model describing the phase separation in the mixture of long rod-like molecules and long chain-like molecules. The model uses the angular distribution function for the orientations of the rods as a dynamical variable. The energetics is based on the nonlocal Onsager theory for the rods combined with a nonlocal extension of the Flory-Huggins theory. The kinetics explicitly takes into account the preferential diffusion along the rods. We computed the phase diagrams in this model and found a number of transitions leading to phase separation. We also performed numerical simulations of the phase separation kinetics and studied the resulting morphologies.