For the past decade, droplet interface bilayers (DIBs) have had an increased prevalence in biomolecular and biophysical literature. However, much of the underlying physics of these platforms is poorly characterized. To further our understanding of these structures, lipid membrane tension on DIB membranes is measured by analysing the equilibrium shape of asymmetric DIBs. To this end, the morphology of DIBs is explored for the first time using confocal laser scanning fluorescence microscopy. The experimental results confirm that, in accordance with theory, the bilayer interface of a volume-asymmetric DIB is curved towards the smaller droplet and a lipid-asymmetric DIB is curved towards the droplet with the higher monolayer surface tension. Moreover, the DIB shape can be exploited to measure complex bilayer surface energies. In this study, the bilayer surface energy of DIBs composed of lipid mixtures of phosphatidylgylcerol (PG) and phosphatidylcholine are shown to increase linearly with PG concentrations up to 25%. The assumption that DIB bilayer area can be geometrically approximated as a spherical cap base is also tested, and it is discovered that the bilayer curvature is negligible for most practical symmetric or asymmetric DIB systems with respect to bilayer area.