Contemporary spintronics devices, notably GMR and TMR-sensors with high linear ranges, stand to benefit from large bias fields in excess of 1T that have been observed in exchange-coupled double layers using rare earth-transition metal ferrimagnets as pinning layers. However, before exploiting the strong coupling the reversal process must be understood at the scales of the smallest devices, where it would be effective. Little is known about these processes to-date, owing to the technical difficulty of imaging magnetic structures smaller than 20nm in fields of several Tesla. Here we image the nanoscale magnetic structures of a double layer comprising a polycrystalline Co/Pt-multilayer (Co/Pt) which is strongly exchange-coupled to an amorphous and magnetically-hard ferrimagnetic TbFe alloy layer. High resolution magnetic force microscopy provides snapshots of the magnetic structures along various applied fields between 0 and 7T as the magnetization reversal takes place. In contrast to a magnetization reversa...