Accurate momentum mapping of bulk and surface electronic states by angle-resolved two-photon photoemission is demonstrated on Cu(111) and one of its vicinal surfaces, Cu(443), using laser light of 3.08 eV photon energy for excitation. The surface state dispersion found agrees well with that expected from the periodic arrangement of terraces and monatomic steps on Cu(443). Polarization dependent data suggest that the state consists of out-of-plane pz orbitals like on the flat (111) copper surface, mixed with in-plane orbitals at the step edges. Maps of the Fermi surface taken from the vicinal surface are found to be in excellent agreement with conventional photoemission data and density-functional calculations. This proves that multiphoton photoemission can be used like direct one-photon photoemission as initial state spectroscopy with high energy and momentum resolution provided that no real intermediate states are involved in the excitation process.