The fast development of microscopy imaging techniques nowadays promotes the generation of a large amount of data. These data are very crucial not only for theoretical biomedical research but also for clinical usage. In order to decrease the inter-intra observer variability and save the human effort on labeling and classifying these images, a lot of research efforts have been devoted to the development of algorithms for biomedical images. Among such efforts, histology image classification is one of the most important areas due to its broad applications in pathological diagnosis such as cancer diagnosis. To improve classification accuracy, most of the previous work focuses on extracting more features and building algorithms for a specific task. This paper proposes a framework based on the novel and robust Collateral Representative Subspace Projection Modeling (C-RSPM) supervised classification model for general histology image classification. In the proposed framework, a cell image is first divided into 25 blocks to reduce the spatial complexity of computation, and one C-RSPM model is built on each block set which contains blocks in the same location from different images. For each testing image, our proposed framework first classifies each of its blocks using the C-RSPM classification model built for that block set, and then applies a multimodal late fusion algorithm with a weighted majority voting strategy to decide the final class label of the whole image. Experimenting using three-fold cross validation with three benchmark histology data sets shows that the proposed framework outperforms other well-known classifiers in the comparison and gives better results than the highest accuracy reported previously.