Magnetic nanostructures reveal unique interface induced properties that differ from those of bulk materials, thus magnetization distributions in interface regions are of high interest. Meanwhile, direct measurement of magnetization distribution in layered nanostructures is a complicated task. Here we study magnetic field induced effects in optical second harmonic generation (SHG) in three-layer ferromagnetic / heavy metals nano films. For a certain experimental geometry, which excludes the appearance of magnetooptical effects for homogeneously magnetized structures, magnetization induced SHG intensity variation is observed. Symmetry analysis of the SHG intensity dependencies on external magnetic field shows that the nonlinear source terms proportional to the out-of-plane gradient component of magnetization govern the observed effect.