Diffusive mixing in a model polymer blend of limited miscibility (i.e., the pair polydimethylsiloxane/polyisobutene) is investigated. The diffusion process is followed in the actual droplet-based microstructure of the polymer blend, as opposed to the ideal planar geometry used in previous studies (Brochard et al. Macromolecules 1983, 16, 1638; Composto et al. Nature 1987, 328, 234). In our experiments we combine Raman microspectroscopy and video particle-tracking microrheology. The first technique allows us to monitor local concentration of the two polymers with high spatial resolution both inside and outside a micrometer-size droplet of the dispersed phase. In addition, microrheology enables to follow how the local viscosity inside the droplet changes during the diffusion. The polymer viscosity inside the droplet is determined by video tracking the Brownian motion of a polystyrene bead microinjected into the droplet. The microspectroscopic and microrheological data are combined to estimate the concentration dependence of the monomer friction factor of the two species, which is a key parameter to calculate the interdiffusion coefficient D. Numerical calculations based on such concentration-dependent interdiffusion coefficient D and several alternative models of the polymer diffusion are compared to the experimental concentration profiles. A satisfactory agreement is found for the so-called "slow theory" (Brochard et al.). A phenomenological model improving the agreement of the model with the experimental data is also presented.