We model how pattern formation in a multicomponent lipid bilayer pinned to an elastic substrate is governed by the interplay between lipid phase separation and the tendency of domains of high intrinsic curvature lipids to deform the membrane away from a stiff substrate such as the cell wall. The emergent patterns, which include compact and striped lipid microdomains, are anticorrelated across the two leaflets and depend on leaflet asymmetry, the ability of lipids to flip between leaflets, and the global geometry. We characterize analytically the dependence of stripe width on lipid parameters, and consider the implications of interleaflet patterning for curvature-dependent lipid localization.