The invention relates to a flexible composite sheet designed to constitute an undersheet behaving as an electromechanical transducer in order to detect the apnea of subjects lying on it. This sheet comprises, in addition to a foil sensitive to pressure in the sense of electromechanical transduction (an electret or polarized piezo-electric foil), two film electrodes and two protective foils. Spacing shims are glued to the two foils against which they are juxtaposed. When the sensitive foil is an electret, the shims are directly interposed between the sensitive foil and one of the two electrodes. When the sensitive foil is a polarized piezo-electric foil, the shims are directly interposed between one of the electrodes and the correspoding external protective foil.