B-cells become activated by ligands with varying valency and mode of presentation to the B-cell receptor (BCR). We previously demonstrated that clustering the immunoglobulin M (IgM) isotype of BCR with an artificial soluble cross-linker stabilized an ordered phase-like domain that enriched kinases and depleted phosphatases to promote receptor tyrosine phosphorylation. BCR is also activated by ligands presented at surfaces, and here we activate B-cells via supported bilayers of phosphatidylcholine lipids, a natural ligand for the IgM BCR expressed in the CH27 cells used. Using superresolution fluorescence localization microscopy, along with a quantitative cross-correlation analysis, we find that BRCs engaged with bilayers sort minimal peptide markers of liquid-ordered and liquid-disordered phases, indicating that ordered-domain stabilization is a general feature of BCR clustering. The phosphatase CD45 is more strongly excluded from bilayer-engaged BRCs than a transmembrane peptide, indicating that mechanisms other than domain partitioning contribute to its organization. Experimental observations are assembled into a minimal model of receptor activation that incorporates both ordered domains and direct phosphatase exclusion mechanisms to produce a more sensitive response.