We present the first examples of thermotropic biaxial mesophases in mixtures of model attractive uniaxial molecules. Nematic and smectic biaxial phases are identified. The nematic biaxial phase has remained a key challenge in the science of liquid crystals since it was first proposed almost 40 years ago. Very recently the first experimental evidence of stable biaxial nematic phases has been obtained in thermotropic liquid crystals of single component biaxial mesogens. Still elusive is the possibility of stabilizing biaxial nematic phases in mixtures of uniaxial particles. We use Monte Carlo molecular simulations to study model mixtures of rodlike and disklike molecules interacting through two intermolecular potential models: one incorporating spherically symmetric (isotropic) attractive interactions; another with anisotropic attractive interactions. These models exhibit nematic and smectic biaxial phases.