Liquid-crystalline phases of stacked lipid bilayers represent a pervasive motif in biomolecular assemblies. Here we report that, in addition to the usual smectic order, multicomponent multilayer membranes can exhibit columnar order arising from the coupling of two-dimensional intralayer phase separation and interlayer smectic ordering. This coupling propagates across hundreds of membrane lamellae, producing long-range alignment of phase-separated domains. Quantitative analysis of real-time dynamical experiments reveals that there is an interplay between intralayer domain growth and interlayer coupling, suggesting the existence of cooperative multilayer epitaxy. We postulate that such long-range epitaxy is solvent-assisted, and that it originates from the surface tension associated with differences in the network of hydrogen-bonded water molecules at the hydrated interfaces between the domains and the surrounding phase. Our findings might inspire the development of self-assembly-based strategies for the long-range alignment of functional lipid domains.