A multicomponent extension of our recent theory of simple fluids [U. M. B. Marconi and S. Melchionna, J. Chem. Phys. 131, 014105 (2009)] is proposed to describe miscible and immiscible liquid mixtures under inhomogeneous, nonsteady conditions typical of confined fluid flows. We first derive from a microscopic level the evolution equations of the phase space distribution function of each component in terms of a set of self-consistent fields, representing both body forces and viscous forces (forces dependent on the density distributions in the fluid and on the velocity distributions). Second, we numerically solve the resulting governing equations by means of the lattice Boltzmann method, whose implementation contains novel features with respect to existing approaches. Our model incorporates hydrodynamic flow, diffusion, surface tension, and the possibility for global and local viscosity variations. We validate our model by studying the bulk viscosity dependence of the mixture on concentration, packing fraction, and size ratio. Finally, we consider inhomogeneous systems and study the dynamics of mixtures in slits of molecular thickness and relate structural and flow properties. (C) 2011 American Institute of Physics. [doi:10.1063/1.3528221]