We put forward a scheme for bridging the length and time scales for soft composite materials consisting of high functionality star polymers and chemically identical polymer chains of smaller size, dissolved into a good or athermal solvent. By employing monomer-level computer simulations and invoking arguments from scaling and Flory theory, we derive realistic effective interactions between the star centers and the midpoint of the chains, which are used as effective coordinates for the mesoscopic description of such mixtures. On the basis of these interactions, we analyze the macroscopic behavior of the same, finding good agreement with previously published experimental results regarding the structure and rheology of this novel type of composite materials. The added chains lead to cluster formation between the stars in a dilute star solution and bring about melting of the star glass at high concentrations of the same. An intriguing insensitivity of the chain-modified star-star effective interaction on the linear polymer concentration is discovered, and the implications of this property are critically discussed.