We have studied the N-dependent switching behavior of composite magnets, comprised of a hard CoPtCr-SiO2 (CPCS) film and a laminated soft [Pt/CPCS]N multilayer. First order reversal curve magnetometry provides evidence of interfacial domain wall (iDW) assisted reversal for N ≥ 5. The magnetic depth profiles determined from polarized neutron reflectometry (PNR) explicitly demonstrate that the composite magnets are more rigidly coupled for N = 3 than for N = 7, and suggest that for N = 7 reversal occurs via formation of iDW. By fitting the PNR profile into the energy surface calculations, we can further deduce the vertical coupling strength in the laminated soft layer.