A simple mean field theory is introduced to describe a biaxial nematic phase in mixtures of a low-molecular-weight liquid crystalline molecule (LC) and a rigid-rodlike polymer (ROD), such as carbon nanotubes (CNTs) and liquid crystalline polymers. When the two components favor perpendicular orientations, we predict a biaxial nematic phase on the temperature-concentration plane, depending on the anisotropic interaction between ROD and LC.