A thermodynamic model is proposed for describing phase diagrams of mixtures of lipid bilayers and amphiphilic proteins or polypeptides in water solution. The basic geometrical variables of the model are the thickness of the hydrophobic region of the lipid bilayer and the length of the hydrophobic region of the proteins. The model incorporates the elastic properties of the lipid bilayer and the proteins, as well as indirect and direct lipid-protein interactions expressed in terms of the geometrical variables. The concept of mismatch of the hydrophobic regions of the lipids and proteins is an important ingredient of the model. The general phase behavior is calculated using simple real solution theory. The phase behavior turns out to be quite rich and is used to discuss previous experiments on planar aggregations of proteins in phospholipid bilayers and to propose a systematic study of synthetic amphiphilic polypeptides in bilayers of different thicknesses. The model is used to interpret the influence of the lipid-protein interaction on calorimetric measurements and on local orientational order as determined by deuterium nuclear magnetic resonance.