A statistical mechanical analysis of the configurations of the fatty acyl chains of N-lignocerylsphingosinephosphorylcholine (n-C 24) and N-palmitoylsphingosinephosphorylcholine (n-C 16) is presented for the case of planar multibilayers. The configurations of the chains are constrained to lie on a three-dimensional lattice, and are generated by the three-dimensional paths of a specified unrestricted random walk on a two-dimensional square lattice. The order-disorder phase transition undergone by the fatty acyl chains is analyzed in light of the model. The transition temperature and enthalpies of transition are predicted in good agreement with calorimetric data. The experimental melting curve of (n-C 24) as measured by Raman spectroscopy, displays a post-transitional melting phenomenon indicative of excess trans bonds persisting beyond the main transition. This particular thermal behavior, absent in n-C 16 is explained with the aid of our theory. In particular, the theoretically predicted ratios of the high temperature (fluid) to the low temperature (gel) melting curve slopes agree very well with the experimental values for n-C 24 and n-C 16. The n-C 24 molecules are predicted to be interdigitated in the gel phase. We discuss the use of our model to predict the equilibrium configurations of fatty acyl chains in membranes in the presence of unsaturated carbon-carbon bonds.