In this Letter, we show how the grooved helical structure of actin microfilaments (F-actin) interacting with mixed fluid lipid bilayers leads to handedness-independent 1D lipid bilayer undulations coupled to longitudinal in-plane ordering of the microfilaments. This longitudinal ordering is forced by the emerging in-plane compression and curvature energy terms of the straight 1D bilayer undulation wave fronts. Thereby, adjacent helices are set into registry along their long axis in their monolayer and pi shifted between adjacent monolayers. An ordered composite multilamellar structure emerges by alternate stacking of these lipid bilayers and monolayers of F-actin. This two-dimensionally ordered system has the symmetries of a centered rectangular columnar liquid crystal, the straight 1D wave fronts playing the role of the classical molecular columns. DOI: 10.1103/PhysRevLett.110.048102