We calculate the nonlinear magneto-optical response of free-standing fcc (001), (110) and (111) oriented Fe monolayers. The bandstructures are determined from first principles using a full-potential LAPW method with the additional implementation of spin-orbit coupling. The variation of the spin-orbit coupling strength and the nonlinear magneto-optical spectra upon layer orientation are investigated. We find characteristic differences which indicate an enhanced sensitivity of nonlinear magneto-optics to surface orientation and variation of the in-plane lattice constants. In particular the crossover from onedimensional stripe structures to twodimensional films of (111) layers exhibits a clean signature in the nonlinear Kerr-spectra and demonstrates the versatility of nonlinear magneto-optics as a tool for in situ thin-film analysis.