We have developed a new and improved optical model of reflection interference contrast microscopy (RICM) to determine with a precision of a few nanometers the absolute thickness h of thin films on a flat surface in immersed conditions. The model takes into account multiple reflections between a planar surface and a multistratified object, finite aperture illumination (INA), and, for the first time, the polarization of light. RICM intensity I is typically oscillating with h. We introduce a new normalization procedure that uses the intensity extrema of the same oscillation order for both experimental and theoretical intensity values and permits us to avoid significant error in the absolute height determination, especially at high INA. We also show how the problem of solution degeneracy can be solved by taking pictures at two different INA values. The model is applied to filled polystyrene beads and giant unilamellar vesicles of radius 10-40 microm sitting on a glass substrate. The RICM profiles I(h) can be fitted for up to two to three oscillation orders, and extrema positions are correct for up to five to seven oscillation orders. The precision of the absolute distance and of the shape of objects near a substrate is about 5 nm in a range from 0 to 500 nm, even under large numerical aperture conditions. The method is especially valuable for dynamic RICM experiments and with living cells where large illumination apertures are required.