Switching behavior in electron-hole bilayer tunnel FETs is known to be unaffected by the subthreshold swing limitation of 60 mV/decade imposed by thermal injection, due to the band-to-band tunneling phenomena on which they rely. However, in this paper, we show that, once parasitic lateral tunneling processes are suppressed by means of heterogate configurations, a new physical limitation arises at the onset of tunneling in this type of transistors, resulting from the interplay between field-induced quantum confinement and asymmetric concentrations of electrons and holes inside the channel. We demonstrate that this limitation comes from the fact that, regardless of the band profile sharpness, the tunneling distance at subband alignment cannot be reduced beyond a certain limit, which we find to be dependent on the body thickness and the material properties.