A patterned perpendicular magnetic recording medium has discrete magnetic islands, each of which has a recording layer (RL) structure that comprises two exchange-coupled ferromagnetic layers. The RL structure may be an “exchange-spring” RL structure with an upper ferromagnetic layer (MAG2), sometimes called the exchange-spring layer (ESL), ferromagnetically coupled to a lower ferromagnetic layer (MAG1), sometimes called the media layer (ML). The RL structure may also include a coupling layer (CL) between MAG1 and MAG2 that permits ferromagnetic coupling. The interlayer exchange coupling between MAG1 and MAG2 may be optimized, in part, by adjusting the materials and thickness of the CL. The RL structure may also include a ferromagnetic lateral coupling layer (LCL) that is in contact with at least one of MAG1 and MAG2 for mediating intergranular exchange coupling in the ferromagnetic layer or layers with which it is in contact (MAG2 or MAG1). The ferromagnetic alloy in the LCL has significantly greater intergranular exchange coupling than the ferromagnetic alloy with which it is in contact (MAG2 or MAG1).