The electron-hole bilayer tunnel (EHBTFET). has been proposed as a density of states (DOS) switch capable of achieving a subthreshold slope lower than 60mV/decade at room temperature; however, one of the main challenges is the control of the lateral band-to-band tunneling (BTBT) leakage in the OFF state. In this work, we show that by using oppositely doped underlap regions; the unwanted penetration of the wavefunction into the underlap region at low gate biases is prevented; thereby drastically reducing the lateral BTBT leakage without any penalty on the ON current. The method is verified using a full-quantum 2D Schrodinger-Poisson solver under the effective mass approximation. For a channel thickness of 10 nm, an In0.53Ga0.47As EHBTFET with counterdoping can exhibit an ON-current up to 20 mu A/mu m and an average subthreshold swing (SS) of about 30 mV/dec. Compared to previous lateral leakage suppression solutions, the proposed method can be fabricated using template-assisted selective epitaxy.