Multilayered thin-him structures consisting of soft magnetic layers and well conducting spacers exhibit high sensitivity to external magnetic fields. We develop the model theory of giant magneto-impedance in such a structure. Expressions for the tensor of surface impedance are obtained and the: problem of sandwich miniaturization under conditions which keep the sensitivity is analysed. The effect of giant magneto-impedance manifests itself in miniaturized sandwiches largely in non-diagonal components. The effect of nondiagonal magneto-impedance shows promise as a basis for developing submicrometre highly sensitive magnetic sensors.