The mechanism of countergradient diffusion of chemical species and heat in turbulent combustion is sought with the aid of the results by the two-scale direct-interaction approximation. The deviation of the Reynolds stress and the turbulent fluxes of chemical species, heat, and mass from their gradient-diffusion representations is related to the Lagrange derivatives of mean velocity and scalars. Their relative magnitude to the gradient-diffusion parts paves the way for explaining the countergradient diffusion. Towards engineering applications, these theoretical findings are converted to a Reynolds-averaged model. It consists of a closed system of equations for the mean density, the mean velocity, the mean internal energy, and the mean scalar, with the turbulence equations for the kinetic energy and its dissipation rate supplemented. This system is tested in a turbulent premixed flame and is shown to reproduce some of the characteristics pointed out by the direct numerical simulation.