We apply a general density functional approach for calculating the force between two big particles immersed in a solvent of smaller ones to calculate the solvent-mediated (SM) potential between two big Gaussian core particles in a binary mixture of smaller Gaussian particles, a simple model of polymers in solution. Within a mean-field free-energy functional, which generates the random phase approximation (RPA) for the bulk pair direct correlation functions, the binary solvent exhibits fluid-fluid phase separation and we show that the theory for calculating the SM potential captures effects of thick adsorbed films surrounding the big solute particles. For a single big particle there is a first-order thin-thick adsorbed film transition and in the thick-film regime-i.e., for solvent-state points lying close to the binodal, on the side where the solvent is poor in the species which is favored by the big particles-we find extremely attractive, long-ranged SM potentials between the big particles whose range is determined by the film thickness. For state points away from the binodal in the thin film regime, or above the "wetting point", the SM potentials are short ranged and less attractive. We show that the effects of the thick adsorbed films around the big particles are not included when the SM potential is obtained from the big-big radial distribution function g(bb)(r), calculated using the RPA closure to the Ornstein-Zernike equations. In the region of the solvent critical point we also find extremely attractive SM potentials whose range is now set by the bulk correlation length in the binary solvent and which increases and eventually diverges for state points approaching the critical point. We calculate the excess chemical potential of the big solute particle in the binary solvent as a function of the concentration of one of the smaller species and show that this quantity also reflects the formation of thick adsorbed films. The form of the excess chemical potential and, hence, the solvation for the soft Gaussian core fluid is contrasted with that expected for a hard-core solute. (C) 2003 American Institute of Physics.