An ability to develop sequence-defined synthetic polymers that both mimic lipid amphiphilicity for self-assembly of highly stable membrane-mimetic 2D nanomaterials and exhibit protein-like functionality would revolutionize the development of biomimetic membranes. Here we report the assembly of lipid-like peptoids into highly stable, crystalline, free-standing and self-repairing membrane-mimetic 2D nanomaterials through a facile crystallization process. Both experimental and molecular dynamics simulation results show that peptoids assemble into membranes through an anisotropic formation process. We further demonstrated the use of peptoid membranes as a robust platform to incorporate and pattern functional objects through large side-chain diversity and/or co-crystallization approaches. Similar to lipid membranes, peptoid membranes exhibit changes in thickness upon exposure to external stimuli; they can coat surfaces in single layers and self-repair. We anticipate that this new class of membrane-mimetic 2D nanomaterials will provide a robust matrix for development of biomimetic membranes tailored to specific applications.