The laser-driven acceleration of high quality proton beams from a double-layer target, comprised of a high-Z ion layer and a thin disk of hydrogen, is investigated with three-dimensional particle-in-cell simulations for an obliquely incident laser pulse. The proton beam energy reaches its maximum at a certain incidence angle, where it can be much greater than the energy at normal incidence. The proton beam propagates at some angle with respect to the target surface normal and with some tilt around the target surface, as determined by the proton energy and the incidence angle.