A cellular membrane, primarily a lipid bilayer, surrounds the internal components of a biological cell from the external components. This self-assembled bilayer is known to be perturbed by ionic liquids (ILs) causing malfunctioning of a cellular organism. In the present study, surface-sensitive X-ray scattering techniques have been employed to understand this structural perturbation in a lipid multilayer system formed by a zwitterionic phospholipid, 1,2-dipalmitoyl--glycero-3-phosphocholine. The ammonium and phosphonium-based ILs with methanesulfonate anions are observed to induce phase-separated domains in the plane of a bilayer. The lamellar X-ray diffraction peaks suggest these domains to correlate across the bilayers in a smectic liquid crystalline phase. This induced IL-rich lamellar phase has a very low lamellar repeat distance, suggesting the formation of an interdigitated bilayer. The IL-poor phase closely related to the pristine lipid phase shows a decrement in the in-plane chain lattice parameters with a reduced tilt angle. The ammonium and phosphonium-based ILs with a relatively bulky anion, -toluenemethanesulfonate, have shown a similar effect.