We present the application of reflection interference contrast microscopy (RICM) (1) to map the optical density of supported bilayers and vesicles and (2) to image the contact profile of phospholipid vesicles at surfaces. The resolution in the surface profile is 0.2 $\mu$m laterally and 1 nm out of plane. The optical thickness of the membrane can be determined with 0.2 nm accuracy. We outline the theoretical basis of RICM and derive the interference intensities of adhering vesicles from first principles. An analytical expression for the decaying contrast of the intrference fringes is given. The contact contour of vesicles is determined for various substrates. We further demonstrate that deposition of a magnesium fluoride layer on the glass substrate enhances the contrast and allows the optical density of adsorbed membranes to be imaged. By contrast variation of the buffer solution, the layer thicknesses and the indices of refraction can be measured. The novel method was applied to image lipid domains of different chain lengths in a substrate supported monolayer.