Some polycrystalline ferromagnetic mms are composed of continuously connected nanometer scale islands with random crystallite orientations. The nanometer perturbations of the mm introduce a large number of nearly degenerate local field configurations that are indistiguishable on a macroscopic scale. As a first step, this situation is modelled as a thin ferromagnetic disc coupled by exchange and dipole interactions to a homogeneous ferromagnetic plane, where the disc and plane have different easy axes. The model is solved to find the partial $Nacute{e}el$ domain walls that minimize the magnetic energy. The two solutions give a bistable configuration that, for appropriate geometries, provides an important microsopic ferromagnetic degree of freedom for the mm. These results are used to interpret recent measurements of exchange biased bilayer films.