We describe a microscope-based optical setup that allows us to perform space- and time-resolved measurements of the spectral reflectance of transparent substrates coated with ultrathin films. This technique is applied to investigate the behavior in water of thermosensitive polymer brushes made of poly(N-isopropylacrylamide) grafted on glass. We show that spectral reflectance measurements yield quantitative information about the conformation and axial structure of the brushes as a function of temperature. We study how parameters such as grafting density and chain length affect the hydration state of a brush, and provide one of the few experimental evidences for the occurrence of vertical phase separation in the vicinity of the lower critical solution temperature of the polymer. The origin of the hysteretic behavior of poly(N-isopropylacrylamide) brushes upon cycling the temperature is also clarified. We thus demonstrate that our optical technique allows for in-depth characterization of stimuli-responsive polymer layers, which is crucial for the rational design of smart polymer coatings in actuation, gating, or sensing applications.