A two-fluid lattice Boltzmann model for binary mixtures is developed. The model is derived formally from kinetic theory by discretizing two-fluid Boltzmann equations in which mutual collisions and self-collisions are treated independently. In the resulting lattice Boltzmann model, viscosity and diffusion coefficients can be varied independently by a suitable choice of mutual- and self-collision relaxation-time scales. Further, the proposed model can simulate miscible and immiscible fluids by changing the sign of the mutual-collision term. This is in contrast to most existing single-fluid lattice Boltzmann models that employ a single-relaxation-time scale and hence are restricted to unity Prandtl and Schmidt numbers. The extension of binary mixing model to multiscalar mixing is quite straightforward.