A model considering both rodlike molecules and platelike molecules is presented in this paper. The model is treated in the framework of a Landau mean-field theory and renormalization group theory. Mean-field theory predicts the transition between the isotropic, rod nematic, plate nematic, and biaxial nematic phases. The renormalization group analysis shows that the transition exhibits a multiphase bicritical point for n (dimensionality of the order parameter) less than or equal to 2. However, for n > 2, the transition exhibits a tetracritical point and an intermediate biaxial nematic phase can exist. The critical exponents are calculated to first order in epsilon (=4-d).