Target-normal sheath acceleration (TNSA) of monoenergetic proton bunches using a triple-layer target consisting of a long slightly-above-critical-density carbon preplasma, a thin solid-density carbon main target layer, and a thin hydrogen layer attached to its back, is considered. The target-back space-charge field the consists of mainly the preplasma electrons that have been accelerated and heated by the relativistic laser pulse. The backside electron cloud is thus denser and more favorably profiled for TNSA of the protons from the hydrogen layer. It is found that a proton beam with a ∼460  MeV monoenergetic peak energy can be generated. The corresponding energy and angular spread are ∼33  MeV and ∼3°, respectively.