In this paper we introduce a novel and accurate optimisation method for segmentation of cardiac MR (CMR) images in patients with pulmonary hypertension (PH). The proposed method explicitly takes into account the image features learned from a deep neural network. To this end, we estimate simultaneous probability maps over region and edge locations in CMR images using a fully convolutional network. Due to the distinct morphology of the heart in patients with PH, these probability maps can then be incorporated in a single nested level set optimisation framework to achieve multi-region segmentation with high efficiency. The proposed method uses an automatic way for level set initialisation and thus the whole optimisation is fully automated. We demonstrate that the proposed deep nested level set (DNLS) method outperforms existing state-of-the-art methods for CMR segmentation in PH patients.