sp² carbon-conjugated covalent organic frameworks (sp²c-COFs) with superb in-plane π-conjugations, high chemical stability, and robust framework structure are expected to be ideal films/membranes for a wide range of applications including energy-related devices and optoelectronics. However, so far, sp²c-COFs have been mainly limited to microcrystalline powders, and this consequently hampered their performances in devices. Herein, we report a simple and robust methodology to fabricate large-area, free-standing, and crystalline sp²c-COF films (TFPT-TMT and TB-TMT) on various solid substrates (e.g., fluorine-doped tin oxide, aluminum sheet, polyacrylonitrile membrane) by self-assembly monolayer-assisted surface-initiated Schiff-base-mediated aldol polycondensation (namely, SI-SBMAP). The resultant sp²c-COF films show lateral sizes up to 120 cm² and tunable thickness from tens of nanometers to a few micrometers. Owing to the robust framework and highly ordered quasi-1D channels, the sp²c-COF membrane-based osmotic power generator presents an output power density of 14.1 W m^-2 under harsh conditions, outperforming most reported COF membranes as well as commercialized benchmark devices (5 W m^-2). This work demonstrates a simple and robust interfacial methodology for the fabrication of sp²c-COF films/membranes for green energy applications and potential optoelectronics.