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 Ne'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.