  The antisymmetric Dzyaloshinskii-Moriya interaction (DMI) in
noncentrosymmetric systems leads to various nonuniform chiral magnetic
textures. Polarized neutron scattering is a powerful method for investigation
such chiral distributions. The most used technique is a small-angle neutrons
scattering (SANS). Multilayered magnetic films with the interface induced DMI
(iDMI) can't be investigated by SANS because of their small volume. The
appropriate technique is a polarized neutron reflectometry. Within the
framework of the continuum theory of micromagnetics, we explore the impact of
the iDMI on the polarized neutrons reflection from multilayers with random
magnetic anisotropy. It is shown that the iDMI gives rise to a
polarization-dependent asymmetric term in the reflection.
