A recent theory [Metlov and Michels, Phys. Rev. B 91, 054404 (2015)PRBMDO1098-012110.1103/PhysRevB.91.054404] predicts a qualitative effect in the magnetic small-angle neutron scattering (SANS) cross section of statistically isotropic disordered ferromagnetic media. The effect is due to the third-order terms in the amplitude of the inhomogeneities. Here, its existence is demonstrated both numerically via large-scale micromagnetic simulations and analyzed experimentally in a two-phase iron-based nanocomposite. The previous model is extended to an arbitrary spatial defect profile, which allows us to describe the experimental field dependence of the third-order SANS effect quantitatively.