Ferri-/ferromagnetic exchange coupled composites are promising candidates for bit patterned media because of the ability to control the magnetic properties of the ferrimagnet by its composition. A micromagnetic model for the bilayer system is presented where we also incorporate the microstructural features of both layers. Micromagnetic finite element simulations are performed to investigate the magnetization reversal behaviour of such media. By adding the exchange coupled ferrimagnet to the ferromagnet, the switching field could be reduced by up to 40% and also the switching field distribution is narrowed. To reach these significant improvements, an interface exchange coupling strength of 2 mJ/m2 is required.