Shape-different molecules are generally incompatible in coassembly due to their different packing preferences.  For example, disk- and rod-shaped molecules in liquid crystalline (LC) phases tend to exclude one another, resulting in macroscopic phase separation.  Here, we report that supramolecular polymerization of a disk-shaped chiral monomer in nematic LC phases comprising rod-shaped molecules results in coassembly, affording a single mesophase with a core–shell columnar geometry.  This LC material is modularly customizable to be responsive to both optical and electrical stimuli, thus realizing the first LC-based optoelectrically operable logic gate device.  The modular strategy allows for cooperative integration of different functions into elaborate dynamic architectures.