We experimentally study the spectra of the transient Faraday and Kerr effects near exciton resonances of a GaAs multiple quantum well. A multilayer calculation with a transfer matrix model accounts quantitatively for the linear transmission (reflectivity) spectra and the Faraday (Kerr) spectra. The Faraday and Kerr spectra do not obey a Kramers-Kronig relation. This phenomenon was found to be due to the multiple reflection effects on the Kerr spectra.