Obtaining high-quality heart and lung sounds enables clinicians to accurately assess a newborn's cardio-respiratory health and provide timely care. However, noisy chest sound recordings are common, hindering timely and accurate assessment. A new Non-negative Matrix Co-Factorisation-based approach is proposed to separate noisy chest sound recordings into heart, lung, and noise components to address this problem. This method is achieved through training with 20 high-quality heart and lung sounds, in parallel with separating the sounds of the noisy recording. The method was tested on 68 10-second noisy recordings containing both heart and lung sounds and compared to the current state of the art Non-negative Matrix Factorisation methods. Results show significant improvements in heart and lung sound quality scores respectively, and improved accuracy of 3.6bpm and 1.2bpm in heart and breathing rate estimation respectively, when compared to existing methods.