Two-dimensional polymers (2DPs) that incorporate molecular hosts offer a distinctive combination of properties, including covalent connectivity, structural regularity, chemical stability, permanent porosity, and molecular recognition. These features make these topologically planar macromolecular sheets promising in relation to applications, including those that appear in sensors, organic electronics, and nanofiltration membranes. Here, we use copper-catalyzed azide-alkyne click chemistry to construct a cyclophane-based 2DP at a liquid-liquid interface by polymerizing a bisazide-functionalized tetracationic cyclophane monomer with a 1,3,5-triethynylbenzene node. The 2DP prepared by employing this strategy is observed to be crystalline porous sheets by a combination of synchrotron X-ray diffraction, transmission electron microscopy, electron diffraction, and nitrogen porosimetry. When employed as the active layer in nanofiltration membranes, this 2DP exhibits excellent rejection performance of a dye, Brilliant Blue G, with 99% of the dye being removed after each cycle. Our findings could lead to the broad application of interfacial click polymerizations to produce 2DPs.