We present the measurement of superconductor/ferromagnetic Josephson junctions, based on an epitaxial Nb bottom electrode and epitaxial Fe20Ni80 barrier. Uniform junctions have been fabricated with a barrier thicknesses in the range 2-12 nm. The maximum critical current density similar to 2.4 +/- 0.2 x 10(9) Am-2 was found for a device with a 3-nm-thick barrier at 4.2 K, corresponding to an average characteristic voltage ICRN similar to 16 mu V. The ICRN showed a nonmonotonic behavior with Fe20Ni80 thickness. The variation of the resistance of a unit area AR(N), of the junctions with barrier thickness gave a Nb/Py specific interface resistance of 6.0 +/- 0.5 f Omega m(2) and Fe20Ni80 resistivity of 174 +/- 50 n Omega m, consistent with other studies in polycrystalline samples.