The mechanics of cellular membranes are governed by a non-equilibrium composite framework consisting of the semiflexible filamentous cytoskeleton and extracellular matrix proteins linked to the lipid bilayer. While elasticity information of plasma membranes has mainly been obtained from whole cell analysis, techniques that allow addressing local mechanical properties of cell membranes are desirable to learn how their lipid and protein composition is reflected in the elastic behavior on local length scales. Introduced here is an approach based on basolateral membranes of polar epithelial Madin-Darby canine kidney (MDCK) II cells, prepared on a highly ordered porous substrate that allows elastic mapping on a submicrometer-length scale. A strong correlation between the density of actin filaments and the measured membrane elasticity is found. Spatially resolved indentation experiments carried out with atomic force and fluorescence microscope permit relation of the supramolecular structure to the elasticity of cellular membranes. It is shown that the elastic response of the pore spanning cell membranes is governed by local bending modules rather than lateral tension.