A backing for an absorptive device such as a disposable diaper or a sanitary napkin, said backing comprising a combination of two layers. The first layer which does not contact the wearer's skin is preferably comprised of a liquid-impervious layer of polymeric film or the like. The second layer is also preferably comprised of a polymeric film which has been made pervious to liquid by providing a multiplicity of relatively small protuberances, each ending in an aperture, substantially across its entire surface. The apertured protuberances, which resemble a tiny volcano in cross-section, exhibit a soft, highly consumer preferred tactile impression which is sometimes characterized as "silky".In backsheets of the present invention, the second layer is oriented so that the tiny volcano-like cusps of the second layer constitute the exposed portion of the backsheet. This minimizes the area of contact between the backsheet and the wearer's skin. In a particularly preferred embodiment of the present invention, the second layer is macroscopically expanded to provide a three-dimensional pattern in its surface, thereby increasing the amount of stand-off between the wearer's skin and the liquid impermeable first layer of the composite backsheet. The tiny apertures in the second layer substantially prevent occlusion of the wearer's skin by providing circulation of air between the first liquid impervious layer of the backsheet of the wearer's skin. This effect is enhanced even further when the first layer is macroscopically expanded to enhance the amount of stand-off between the wearer's skin and the liquid impervious first layer. The reduced contact area and the enhanced air circulation between the backsheet and the wearer's skin reduce the tendency toward perspiration and sticking of the backsheet to the wearer's skin.