We investigate carrier transport in a single 22-nm-thick double-gate Si quantum well device, which has independent contacts to electrons and holes. Conductance, Hall density and Hall mobility are mapped in a broad double-gate voltage window. When the gate voltage asymmetry is not too large only either electrons or holes occupy the Si well and the Hall mobility shows the fingerprints of volume inversion/accumulation. At strongly asymmetric double-gate voltage an electric field induced electron-hole (EH) bilayer is formed inside the well. The EH drag resistance Rhe is explored at balanced carrier densities: Rhe decreases monotonically from 860 to 37 Ω when the electron and hole densities are varied between ∼0.4×1016 and 1.7×1016 m−2.