All-organic three-component composites were fabricated by embedding conductive polyaniline (PANI) into a dielectrically enhanced matrix of poly(vinylidene fluoride-trifluoroethylene- chlorofluoroethylene) [P(VDF-TrFE-CFE)] with both chemically grafted and physically blended copper phthalocyanine oligomer (CuPc). Dielectric behavior of the composites with different volume fraction of dispersed PANI phase can be described by percolation theory. One of such composites with the PANI content close to the percolation threshold (f (c) = 0.146) has a dielectric constant 516 and a loss factor of 0.51 at 100 Hz, and the breakdown field is 28.0 MV/m. The composite remains very flexible with an elastic modulus close to that of the parent copolymer.