To analyze the adsorption of single vesicles composed of two types of lipids (e.g., zwitterionic and positively charged lipids or zwitterionic and negatively charged lipids), we propose a statistical model taking into account lipid-surface interactions, lipid-lipid lateral interactions, and vesicle bending energy. Our treatment specifies how these parameters govern vesicle adsorption, shows how the radius of the vesicle-surface contact area may depend on the vesicle composition, and clarifies the conditions for vesicle rupture.