We have investigated lipid acyl chain order parameters of giant unilamellar vesicles (GUVs) using multiphoton fluorescence microscopy. We compare two widely used models of lipid acyl chain order parameters: the "wobble-on-a-cone" model and the Gaussian distribution model. For the first time, we systematically address a ternary system for which the phase diagram encompassing both composition and temperature space has been mapped in order to determine tie-line directions and thus phase assignment. In addition, because miscibility and chain melting transitions can be observed directly and simultaneously with multiphoton microscopy, our technique is applicable to determining the extent of the coupling between chain order and miscibility; thus, it provides a more robust platform for comparison with theory.