A molecular interaction model is used to describe the phase diagram of two-component phospholipid bilayer membranes of saturated phospholipids, DC_nPC, with different acyl-chain lengths, n = 12,14,18,20. The interaction between acyl chains of different length is formulated in terms of a hydrophobic mismatch which permits the series of binary phase diagrams to be calculated in terms of a single 'universal' interaction parameter. The properties of the model are calculated by computer-simulation techniques which not only permit determination of the specific-heat function and the phase diagram but also reveal the local structure of the mixture in the different parts of the phase diagram. The local structure is described pictorially and characterized quantitatively in terms of a correlation function. It is shown that the non-ideal mixing of lipid species due to mismatch in the hydrophobic lengths leads to a progressively increasing local ordering as the chain-length difference is increased. A pronounced local structure is found to persist deep inside the fluid phase of the mixture. The local structure is discussed in relation to the features observed in the specific-heat function, for which theoretical data, as well as experimental data obtained from differential-scanning calorimetry are presented.