Positron annihilation lifetime spectroscopy (PALS) and differential scanning calorimetry (DSC) were used to study the interdiffusion in a particle-matrix system consisting of the miscible polymers poly(vinyl chloride) (particles) and poly(n-butyl methacrylate) (matrix, 30:70 and 50:50 w/w). Starting from the demixed state of the blends, the transition to the mixed state during annealing at 110 degreesC was investigated. We deliver further evidence that PALS parameters such as the orthopositronium intensity 13 and the average positron lifetime tau(av) respond to chemical inhomogeneities in blends and their disappearance due to mutual diffusion of molecules of both phases. The response is due to inhibition of Ps formation by one of the constituents when its molecules migrate into the phase made from the second one. A core-shell model for the description of the o-Ps response to a local chemical inhomogeneity is developed which makes use of a calculated concentration-distance profile. The comparison with the experiment allows the estimation of the interface width and of kinetic parameters, such as the exponent of the time dependence of the interface width and the coefficient of mutual diffusion. The potential and the limitation of this new technique are discussed.