We present a semi-supervised fine-tuning framework for foundation models that utilises mutual information decomposition to address the challenges of training for a limited amount of labelled data. Our approach derives two distinct lower bounds: i) for the downstream task space, such as classification, optimised using conditional and marginal cross-entropy alongside Kullback-Leibler divergence, and ii) for the latent space representation, regularised and aligned using a contrastive-like decomposition. This fine-tuning strategy retains the pre-trained structure of the foundation model, modifying only a specialised projector module comprising a small transformer and a token aggregation technique. Experiments on several datasets demonstrate significant improvements in classification tasks under extremely low-labelled conditions by effectively leveraging unlabelled data.