In this paper, we propose a decomposition-based weakly-supervised model that utilizes the class labels of the sources present in mixtures. We apply this weak class supervision approach to superimposed handwritten digit images using both non-negative matrix factorization (NMF) and generative adversarial networks (GANs). In this way, we can learn non-linear representations of the sources. The results of our experiments demonstrate that the proposed weakly-supervised methods are viable and mostly on par with the fully supervised baselines. The proposed joint classification and separation approach achieves a weakly-supervised source classification performance of 90.3 in terms of F1 score and outperforms the multi-label source classifier baseline of 68.2 when there are two sources. The separation performance of the proposed method is measured in terms of peak-signal- to-noise-ratio (PSNR) as 16 dB, outperforming the class-informed sparse NMF which achieves separation of two sources with a PSNR value of 13.9 dB. We show that it is possible to replace supervised training with weakly- supervised methods without performance penalty.