2D materials such as graphene exhibit unique electronic and mechanical properties that promise substantial advantages in applications ranging from nanoelectronics to human health. Such interfaces are often functionalized noncovalently with lying-down phases of functional molecules to avoid disrupting electronic structure with the basal plane. Structurally, such molecules are often very similar to amphiphiles found in biological cell membranes, though the overall surface chemistry is strikingly different -- in essence, a repeating cross-section of a lipid bilayer, with both hydrophilic and hydrophobic components exposed at the environmental interface in a structured manner. As 2D materials are integrated into hybrid materials and devices, this functionalization approach raises two classes of significant questions: (1) How do noncovalent lying-down phases of phospholipids and fatty acids respond to solution or thermal processing? More generally, to what extent can structural design principles from the cell membrane be invoked to control chemical functionality and reactions at the interface? (2) Can noncovalently-adsorbed layers be patterned to template further interactions with the environment? Lying-down phases of phospholipids and fatty acids present 1-nm-wide stripes of ordered chemical functional groups, suggesting the possibility of controlling processes such as crystallization, phase segregation, or analyte binding. We examine these questions, again integrating design principles from biological cell membranes, which use hundreds of structurally different amphiphiles to create a complex noncovalent interface of central biological importance.