The ternary system consisting of cholesterol, a saturated lipid, and an unsaturated one exhibits a rich phase behavior with multiple phase coexistence regimes. Remarkably, phase separation even occurs when each of the three binary systems consisting of two of these components is a uniform mixture. We use a Flory-Huggins like model in which the phase separation of the ternary system is a consequence of an interaction between all three components to describe the system. From the associated Gibbs free energy we calculate phase diagrams, spinodals, and critical points. Moreover, we use a Van der Waals/Cahn-Hilliard like construction to derive an expression for the line tension between coexisting phases. We show how the line tension depends on the position in the phase diagram, and give an explicit expression for the concentration profile at the phase boundary.