Using small-angle neutron scattering (SANS) and cyclic voltammetry (CV), we show that model biological membranes can be deposited on a polymer cushion confined in highly regular porous alumina. The thicknesses of the dilute polymer cushion chemically bound to the alumina and of the supported bilayer are obtained for two polyethylene glycol cushions (PEG(5000) and PEG(20000)) and for a cushion made of chains bearing a lipid anchor at their free end (DSPE-PEG(3400)). The bilayers are studied well below and well above the chain melting temperature of the lipid mixture (DMPC/DMPE: 80/20), using a coenzyme (Ubiquinone, UQ(10)) as a redox probe for the voltammetry experiments. Analysis of the SANS form factor of the bilayers shows that the bilayer thickness can be extracted in this particular geometry. Using PEG chains grafted at a low surface density (D < 2R(g)), the thickness of the complete molecular construction is obtained by CV, which shows (after subtracting the bilayer thickness) that the polymer cushion thickness can be varied from 50 to 150 Angstroms. The values obtained with three different chain lengths, are in perfect agreement with the radius derived from the Flory theory.