A new approach to the structure of dispersion-filled polymeric composites as a combination of two fractals (generally, multifractals) – the filler-particle skeleton and the polymeric matrix – is proposed. It is shown that the fractal (Hausdorff) dimensions of these fractals are interrelated. The physical significance of the “disturbance” to the structure of the polymer matrix that results from introduction of the dispersed filler is examined in detail.