Most planetary nebulae (PNe) show beautiful, axisymmetric morphologies despite their progenitor stars being essentially spherical. Close binarity is widely invoked to help eject an axisymmetric nebula, after a brief phase of engulfment of the secondary within the envelope of the Asymptotic Giant Branch (AGB) star, known as the common envelope (CE). The evolution of the AGB would thus be interrupted abruptly, its envelope being rapidly ejected to form the PN, which a priori would be more massive than a PN coming from the same star, were it single. We aim at testing this hypothesis by investigating the mass of a sample of 21 post-CE PNe, ~1/5th of the known total population, and comparing them to a large sample of `regular' (i.e. not known to host close binaries) PNe. We have gathered data on the ionised and molecular content of our sample and carried out new molecular observations. We derive the ionised and molecular masses of the sample by means of a systematic approach, using tabulated, dereddened H-beta fluxes for finding the ionised mass, and CO 2-1 and 3-2 observations for the molecular mass. There is a general lack of molecular content in post-CE PNe, with few exceptions. Once we derive the ionised and molecular masses, we find that post-CE PNe arising from Single-Degenerate (SD) systems are just as massive, on average, as `regular' PNe, whereas post-CE PNe arising from Double-Degenerate (DD) systems are considerably more massive, and show larger linear momenta and kinetic energy than SD systems and `regular' PNe. Reconstruction of the CE of four objects suggests that the mass of SD nebulae actually amounts to a very small fraction of the envelope of their progenitor stars. This leads to the uncomfortable question of where the rest of the envelope is and why we cannot detect it in the stars' vicinity, thus raising serious doubts on our understanding of these intriguing objects.