We present detailed theoretical and experimental analysis of the magneto-op
tic transverse Kerr effect in magnetic multilayers. The theoretical model i
s based upon a phenomenological permittivity tensor. From the general resul
t, suitable only for numerical calculations, we derive several approximate
analytical expressions in order to make a qualitative discussion. The theor
etical predictions are compared with experimental results in Y/Co bilayers,
and the good agreement found allows for an accurate determination of the m
agneto-optical constants of the material. Then, the theoretical model is ap
plied to make a detailed study of interface magnetism in Y1-xCox alloys, an
d to perform numerical simulations in Co/Cu and Fe/Cu multilayers. The resu
lts in multilayers highlight the complex behavior of the magneto-optic tran
sverse Kerr effect, in which the contributions of the individual layers are
never strictly additive. This nonlinearity is found to be strongly depende
nt on the 3d magnetic metal present and could be used to probe the alignmen
t of the layers even in a configuration of vanishing magnetic moment.