A lyotropic inverse micelle phase composed of water, thermotropic liquid-crystal octylcyanobiphenyl (8CB), and surfactant (DDAB) was studied by using high-resolution calorimetry on several mixtures with 3%, 8%, and 15% micelle concentration. Calorimetric results show strong depression of the isotropic to nematic (I-N) phase-transition temperature. Broad heat-capacity anomalies show the existence of a wide coexistence range of isotropic, nematic, and smectic-A phases, which mimics the behavior of a new nearly stable thermodynamic phase. An observation of the rather sharp almost bulklike nematic to smectic-A (N-A) transition at low-temperatures indicates that our heat capacity results are consistent with the phase separation scenario in which significant number of micelles is expelled during I-N conversion leaving almost pure nematic phase at lower temperatures. It was found that micelles get almost completely remixed on heating the mixture back to the isotropic phase.