We explored changes in magnetic domain structures in a magnetic layer due to the onset of the superconductivity of an adjacent superconductive layer using neutron reflectometry. Magnetic domain structures in 1 µm thick permalloy (Py) films were studied as functions of magnetic field, temperature and under the influence of the onset of superconductivity in a neighboring layer. Bragg peaks in the off-specular scattering were observed at low fields following saturation with an in-plane field, which are attributed to the quasi-parallel magnetic stripes along the field direction. During the magnetization reversal from saturation, the stripe pattern shows increases in the period, the transverse coherence length (i.e., perpendicular to the stripes) and the amplitude of the out-ofplane magnetization component. The coherence length of the magnetic stripes is anisotropic in the remnant state with the longitudinal coherence length (i.e., along the stripes) being larger than the transverse one. The stripe period shows a weak temperature dependence between 300 K and 3 K, but no abrupt change in the period is observed when the temperature crosses the superconducting critical temperature.