An analysis is given which predicts that initial permeabilities of the order of a million could be obtained from typical permalloy thin films if these films were in the appropriate type of structure. A three‐layered structure, where a permalloy layer is sandwiched between and exchange‐coupled to a pair of highly anisotropic magnetic layers, can be arranged so that having the outer layers magnetized in opposite directions is a stable magnetic configuration. Because of the exchange coupling, this configuration creates a domain wall in the plane of the permalloy layer. The methods of micromagnetics are applied in this paper to obtain a mathematical analysis of such domain walls, giving the functional dependences of the wall shape and position on the external field, layer thicknesses and magnetic parameters. Numerical results show that typical permalloy layers of several microns in thickness could exhibit initial permeabilities of a million in external fields of the order of millioersteds. Inductor applications of this structure are briefly discussed, where it is concluded that such inductors would have a maximum operating frequency of 105to 106Hz.