This paper addresses the challenge of Multispectral (MS) document image segmentation, which is an essential step for subsequent document image analysis. Most previous studies have focused only on binary (text/non-text) separation. They also rely on handcrafted features and techniques dedicated to conventional images that do not take advantage of MS images’ spectral richness. In this work, we reformulate this task as a source separation problem, whereby we target the blind decomposition of entire MS document images via a new orthogonal nonnegative matrix factorization (ONMF). On the one hand, we incorporate orthogonality constraint as a Riemannian optimization on the Stiefel manifold. On the other hand, based on which factor we impose the orthogonality constraint, i.e., either on the endmember matrix, abundance matrix, or both, we propose three ONMF models to investigate this issue and determine which model is more suitable for this study. Minimizing the three models subject to nonnegativity and orthogonality constraints simultaneously is very challenging. Therefore, we extend the alternating direction method of multipliers scheme to solve them. We evaluated our models on synthetic Hyperspectral (HS) images and real-world MS document images. The experimental results confirm the effectiveness of the proposed models and demonstrate their generalization power compared to state-of-the-art techniques.