Mixing and segregation of granular particles on the basis of size and density from vertical vibration or upward gas flow is critical to a wide range of industrial, agricultural and natural processes. Recently, combined vibration and gas flow under certain conditions has been shown to create periodically repeating structured bubbling patterns within a fluidized bed of spherical, monodisperse particles. Here, we demonstrate with experiments and simulations that structured bubbling can form in binary mixtures of particles with different size and density, but with similar minimum fluidization velocities. Structured bubbling leads to particles mixing regardless of initial particle configuration, while exciting particles with only gas flow produces smaller unstructured bubbles which act to segregate particles. Discrete particle simulations match the experimental results qualitatively and, in some regards quantitatively, while continuum particle simulations do not predict mixing in the case of structured bubbling, highlighting areas for future model improvement.