Vortex structures in the ferromagnet/type-II superconductor bilayer are investigated when the ferromagnet has domain structure and perpendicular magnetic anisotropy. It is found that two equilibrium vortex structures can be realized: straight vortices with alternating directions corresponding to the direction of the magnetization in the ferromagnetic domains and vortex semiloops connecting the ferromagnetic domains with opposite direction of the magnetization. These states are separated by an energy barrier. The values of the critical magnetization for the formation of these vortex structures are determined.