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~$mu$m 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 (textit{i.e.}, perpendicular to the stripes) and the amplitude of the out-of-plane magnetization component. The coherence length of the magnetic stripes is anisotropic in the remnant state with the longitudinal coherence length (textit{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.
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