We present detailed theoretical and experimental analysis of the magneto-optic transverse Kerr effect in magnetic multilayers. The theoretical model is based upon a phenomenological permittivity tensor. From the general result, suitable only for numerical calculations, we derive several approximate analytical expressions in order to make a qualitative discussion. The theoretical predictions are compared with experimental results in Y/Co bilayers, and the good agreement found allows for an accurate determination of the magneto-optical constants of the material. Then, the theoretical model is applied to make a detailed study of interface magnetism in Y 1Ϫx Co x alloys, and to perform numerical simulations in Co/Cu and Fe/Cu multilayers. The results in multilayers highlight the complex behavior of the magneto-optic transverse Kerr effect, in which the contributions of the individual layers are never strictly additive. This nonlinearity is found to be strongly dependent on the 3d magnetic metal present and could be used to probe the alignment of the layers even in a configuration of vanishing magnetic moment.

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