DNA nanotechnology enables the precise construction of nanoscale devices that mimic aspects of natural biomolecular systems yet exhibit robustly programmable behavior. While many important biological processes involve dynamic interactions between components associated with phospholipid membranes, little progress has been made toward creating synthetic mimics of such interfacial systems. We report the assembly and characterization of cholesterol-labeled DNA origami "barges" capable of reversible association with and lateral diffusion on supported lipid bilayers. Using single-particle fluorescence microscopy, we show that these DNA barges rapidly and stably embed in lipid bilayers and exhibit Brownian diffusion in a manner dependent on both cholesterol labeling and bilayer composition. Tracking of individual barges rapidly generates super-resolution maps of the contiguous regions of a membrane. Addition of appropriate command oligonucleotides enables membrane-associated barges to reversibly exchange fluorescent cargo with bulk solution, dissociate from the membrane, or form oligomers within the membrane, opening up new possibilities for programmable membrane-bound molecular devices.