A phenomenological model is proposed to describe the membrane phase equilibria in binary mixtures of saturated phospholipids with different acyl-chain lenghts. The model is formulated in terms of thermodynamic and thermomechanic properties of the pure lipid bilayers, specifically the chain-melting transition temperature and enthalpy, the hydrophobic bilayer thickness, and the lateral area compressibility modulus. The model is studied using a regular solution theory made up of a set of interaction parameters which directly identify that part of the lipid-lipid interaction which is due to hydrophobic mismatch of saturated chains of different lengths. It is then found that there is effectively a single universal interaction parameter which, in the full composition range, describes the phase equilibria in mixtures of DMPC/DPPC, DPPC/DSPC, DMPC/DSPC, and DLPC/DSPC, in excellent agreement with experimental measurements. The model is used to predict the variation with temperature and composition of the specific heat, as well as of the average membrane thickness and area in each of the phases. Given the value of the universal interaction parameter, the model is then used to predict the phase diagrams of binary mixtures of phospholipids with different polar head groups, e.g., DPPC/DPPE, DMPC/DPPE and DMPE/DSPC. By comparison with experimental results for these mixtures, it is shown that difference in acyl-chain lengths gives the major contribution to deviation from ideal mixing. Application of the model to mixtures with non-saturated lipids is also discussed.