Mixtures of polymers with different compositions are of great importance for many technological and industrial applications because as the composition of polymers change, the mixture structure and dynamics can change significantly. Molecular simulations may be used to study polymer mixtures but their properties develop on such an extended range of time and length-scale that they cannot be investigated by atomistic simulations. In this regard, the integral equation coarse-graining (IECG) approach has been developed in which the polymers are either represented as soft spheres or multi coarse-graining (CG) sites, where each CG site consists of a large enough number of monomers to use Gaussian statistics to obtain the intramolecular correlations. The IECG method is based on the liquid state theory and solves the Ornstein-Zernike equation to obtain the intermolecular correlations, and consequently the effective CG potentials. Representing polymer melts with a given degree of polymerization at various resolutions, we use the IECG theory and/or perform the IECG simulations to investigate the properties of the same polymer melt represented by mixtures of CG models at various resolutions. We show that the structural and thermodynamical properties, such as pressure and pair correlation functions, for such mixtures are consistent with pure CG liquids as well as the underlying atomistic simulations. We also address the compositional dependence of the effective IECG potential, along with its range for various types of mixtures.