Microstructure of materials is often characterized through image analysis to understand processing-structure-properties linkages. We propose a largely automated framework that integrates unsupervised and supervised learning methods to classify micrographs according to microstructure phase/class and, for multiphase microstructures, segments them into different homogeneous regions. With the advance of manufacturing and imaging techniques, the ultra-high resolution of imaging that reveals the complexity of microstructures and the rapidly increasing quantity of images (i.e., micrographs) enables and necessitates a more powerful and automated framework to extract materials characteristics and knowledge. The framework we propose can be used to gradually build a database of microstructure classes relevant to a particular process or group of materials, which can help in analyzing and discovering/identifying new materials. The framework has three steps: (1) segmentation of multiphase micrographs through a recently developed score-based method so that different microstructure homogeneous regions can be identified in an unsupervised manner; (2) {identification and classification of} homogeneous regions of micrographs through an uncertainty-aware supervised classification network trained using the segmented micrographs from Step $1$ with their identified labels verified via the built-in uncertainty quantification and minimal human inspection; (3) supervised segmentation (more powerful than the segmentation in Step $1$) of multiphase microstructures through a segmentation network trained with micrographs and the results from Steps $1$-$2$ using a form of data augmentation. This framework can iteratively characterize/segment new homogeneous or multiphase materials while expanding the database to enhance performance. The framework is demonstrated on various sets of materials and texture images.