How the distinctive lipid composition of mammalian plasma membranes impacts membrane protein structure is largely unexplored, partly because of the dearth of isotropic model membrane systems that contain abundant sphingolipids and cholesterol. This gap is addressed by showing that sphingomyelin and cholesterol-rich (SCOR) lipid mixtures with phosphatidylcholine can be cosolubilized by n-dodecyl-β-melibioside to form bicelles. Small-angle X-ray and neutron scattering, as well as cryo-electron microscopy, demonstrate that these assemblies are stable over a wide range of conditions and exhibit the bilayered-disc morphology of ideal bicelles even at low lipid-to-detergent mole ratios. SCOR bicelles are shown to be compatible with a wide array of experimental techniques, as applied to the transmembrane human amyloid precursor C99 protein in this medium. These studies reveal an equilibrium between low-order oligomer structures that differ significantly from previous experimental structures of C99, providing an example of how ordered membranes alter membrane protein structure.