Independently exchange biased subsystems can coexist in ferromagnet/antiferromagnet bilayers after various field-cooling protocols. We find well separated double hysteresis loops in FeF2/Ni bilayers for intermediate cooling fields, while for small or large cooling fields a negatively or positively shifted single loop, respectively, are encountered. The antiferromagnet breaks into a bidomain state with opposite signs but equal magnitude of bias acting on the ferromagnet. This idea is supported by micromagnetic simulations. Experiments are presented, where thermally activated motion of these antiferromagnetic domain boundaries can be achieved.