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Membranes serve diverse functions in biological systems. Variations in their molecular compositions impact their physical properties and lead to rich phase behavior such as switching from the gel to fluid phase and/or separation to micro- and macrodomains with different molecular compositions. We present a combined computational and experimental study of the phase behavior of a mixed membrane of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC) molecules. This heterogeneous membrane changes from gel to fluid and shows separate domains as a function of temperature. Atomically detailed simulations provide microscopic information about these molecular assemblies. However, these systems are challenging for computations since approaching equilibrium necessitates exceptionally long molecular dynamics trajectories. We use the simulation method of MDAS (Molecular Dynamics with Alchemical Steps) to generate adequate statistics. Isotope-edited IR spectroscopy of the lipids was used to benchmark the simulations. Together, simulations and experiments provide insight into the structural and dynamical features of the phase diagram.