In proton acceleration from laser-irradiated thin foil targets, adding foams on the front surface or connecting a helical coil on the rear surface of the foil has proven to be an effective scheme to enhance proton energy. In this paper, we make the first attempt to incorporate the above two enhancement schemes for laser-proton acceleration by simultaneously adding foams and connecting a helical coil to a thin foil target. By utilizing such integrated targets in the experiment, focused beams were generated. The maximum proton energy and the number of energetic protons are apparently enhanced. Moreover, quasi-monoenergetic peaks were formed at the high-energy end of the spectra. Particle-in-cell plasma simulations and electromagnetic beam dynamics simulations show that the double-layer target not only enhances the energy of protons but also leads to a multiple-fold increase in the number of escaped electrons, which results in an enhanced post-acceleration in helical coil subsequently.