A reflectance difference spectroscopy (RDS) microscope with 3-nm step height resolution and subwavelength lateral resolution for exposed surfaces and 5-nm step height resolution for interfaces 45 nm beneath a transparent layer with smooth surface, is demonstrated. It has extremely high tolerance to optical path drift (up to 3.7 mum at wavelength of 512 nm), high tolerance to power fluctuation (~5%), and a long working distance (8 mm). Better height resolution can be achieved with higher laser power. The RDS signal that reveals the presence of the edges is due to the depolarization of light caused by scattering by the edges, so edges of any orientation can be detected with equal sensitivity without the need to rotate the sample.