Scanning transmission X-ray microscopy (STXM), atomic force microscopy (AFM), near-edge X-ray absorption fine structure (NEXAFS) spectroscopy, and photoemission electron microscopy (PEEM) were used to obtain the three-dimensional concentration profiles and the late-stage morphology of liquid bilayer thin films of the two imiscible polymers polystyrene (PS) and (polybromostyrene) (PBrx=0.79S), where x fraction of monomers brominated) as a function of the lower PS film thickness. The results showed that the apparent contact angle at the polymer/air interface decreases exponentially with increasing PS film thickness with a constant that scales with the PS radius of gyration (R-g) In contrast, the Neuman angle, as determined from the PBrS STXM images, increases with substrate thickness. NEXAFS and PEEM data show that the droplets consist of a PBrS core fully encapsulated by PS for substrate thicknesses greater than R-g. Only partial encapsulation is seen for substrates less than R-g. These results could not be explained with existing models developed for bulk viscoelastic fluids. We found that, for the case of entangled polymers, other factors such as the interfacial energy with the substrate, the film thickness, and the molecular weights must be considered. A model which includes a restoring force characterizing the change in stiffness of the substrate layer due to surface interactions provided good agreement with the experimental observations.