A novel method was developed to measure the local curvatures of phase-separating interface, i.e., the mean and Gaussian curvatures, from three-dimensional (3D) digital images of the bicontinuous domain structures formed during a phase-separation process via spinodal decomposition (SD). One of the aims of the study is to quantify the local geometry of the interface and its time evolution. Distributions of the interfacial curvatures were obtained by calculating the curvatures at many points on the interface. The applicability and precision of the method were critically tested using various model surfaces, e.g., spheres, cylinders, ellipsoids of revolution, and an infinite periodic minimal surface (IPMS), Schoen's gyroid. The method was then applied to the 3D interface developed via SD of a polymer blend. It was found that the interface of the polymer blend (i) was, for the most part, hyperbolic and (ii) had a considerably broader curvature distribution than that of Schoen's gyroid, though area-averaged curvatures obtained in our previous study had the same characteristics as IPMS.