Confounding bias is a crucial problem when applying machine learning to practice, especially in clinical practice. We consider the problem of learning representations independent to multiple biases. In literature, this is mostly solved by purging the bias information from learned representations. We however expect this strategy to harm the diversity of information in the representation, and thus limiting its prospective usage (e.g., interpretation). Therefore, we propose to mitigate the bias while keeping almost all information in the latent representations, which enables us to observe and interpret them as well. To achieve this, we project latent features onto a learned vector direction, and enforce the independence between biases and projected features rather than all learned features. To interpret the mapping between projected features and input data, we propose projection-wise disentangling: a sampling and reconstruction along the learned vector direction. The proposed method was evaluated on the analysis of 3D facial shape and patient characteristics (N = 5011). Experiments showed that this conceptually simple method achieved state-of-the-art fair prediction performance and interpretability, showing its great potential for clinical applications.