Pulse laser deposited La2/3Sr1/3MnO3 ultrathin films on SrTiO3 substrates were characterized by polar and longitudinal Kerr magneto-optical spectroscopy. Experimental data were confronted with theoretical simulations based on the transfer matrix formalism. An excellent agreement was achieved for a 10.7 nm thick film, while a distinction in the Kerr effect amplitudes was obtained for a 5 nm thick film. This demonstrated the suppression of ferromagnetism due to the layer/substrate interface effects. A revised, depth-sensitive theoretical model with monolayer resolution described the experimental data well, and provided clear cross-section information about the evolution of ferromagnetism inside the film. It was found that the full restoration of the double-exchange mechanism, responsible for the ferromagnetic ordering in La2/3Sr1/3MnO3, occurs within the first nine monolayers of the film. Moreover, all the studied films exhibited magneto-optical properties similar to bulk crystals and thick films. This confirmed a fully developed perovskite structure down to 5 nm.