A suspension of rodlike colloidal particles and rodlike liquid crystalline polymers is modeled as a mixture of thick (colloidal) and thin (polymeric) rods. The model mixture is studied by means of an Onsager type, theory, the colloidal particles are represented by hard rods and the polymer by hard rods with zero diameter. Extensive immiscibility is observed for the colloid plus polymer model mixture and if the polymer is more than 3 times as long as the colloid coexistence between two isotropic phases is observed. For all polymer lengths phase separation into an almost pure ideal gas df polymer and a dense nematic phase of colloid is observed at high polymer fugacity. The phase separation is driven by excluded volume effects; the volume available to the polymer is maximized by separating from the colloid.