The multi-channel nature of digital histopathological images presents an opportunity to exploit the correlated color channel information for better image modeling. Inspired by recent work in sparsity for single channel image classification, we propose a new simultaneous sparsity model for multi-channel histopathological image representation and classification (SHIRC). Essentially, we represent a histopathological image as a sparse linear combination of training examples under suitable channel-wise constraints. Classification is performed by solving a newly formulated simultaneous sparsity-based optimization problem. A practical challenge is the correspondence of image objects (cellular and nuclear structures) at different spatial locations in the image. We propose a robust locally adaptive variant of SHIRC (LA-SHIRC) to tackle this issue. Experiments on two challenging real-world image data sets: 1) mammalian tissue images acquired by pathologists of the animal diagnostics lab (ADL) at Pennsylvania State University, and 2) human intraductal breast lesions, reveal the merits of our proposal over state-of-the-art alternatives. Further, we demonstrate that LA-SHIRC exhibits a more graceful decay in classification accuracy against the number of training images which is highly desirable in practice where generous training per class is often not available.