Sulfonated polyurethane (PUI, matrix) is synthesized and composited with polyacene quinone radical polymers (PAQRs, filler). The polarization mechanism of these polymers and composites were investigated in terms of their frequency, temperature, and filler-concentration-dependent dielectric properties. We found that PUI/PAQR composites have a high permittivity, which is attributed to the filler-matrix interfacial polarization and the contact effect. The PAQR-concentration-dependent permittivity of different PUI/PAQR composites reveals a percolation threshold at 20-30 wt % with scaling exponents that indicate the intercluster polarization. The frequency dependence of dielectric response is well-fitted by using the Debye and Cole-Cole functions on the basis of the structural diagrams and equivalent circuit, leading to a detailed evaluation on heterogeneous structures of different PUI/PAQR composites.