A new type of wall coupling previously considered implausible has been observed in coupled Permalloy films 2000 Å thick and 2 microns apart. The walls separate antiparallel domains oriented along the easy axis and zigzagging perpendicularly to it. A model for the magnetization distribution in the transition region between oppositely magnetized domains has been proposed for the evaluation of the magnetostatic interaction between superposed wall segments of the two films. The width of the transition regions and the angles formed with the easy axis have been calculated by minimizing the total free energy. The analytical results agree with the experimental values obtained from a dual beam Kerr apparatus monitoring the top and bottom films. Measured mobilities using interrupted pulses gave values in the range of cm/s.Oe.