Large-scale and up-to-date canopy height model (CHM) estimates are key to forest resources assessment and disturbance analysis. In this work we present an investigation of the potential of Deep Learning (DL) for the regression of forest height from TanDEM-X bistatic InSAR data. We propose a novel fully convolutional neural network (CNN) framework, trained and tested on four tropical sites in Gabon, Africa, together with a series of experiments for assessing the impact of different input features with specific focus on bistatic InSAR. The obtained results are extremely promising and already in line with state-of-the-art methods based on theoretical modelling, with the remarkable advantage of requiring only one single TanDEM-X acquisition at inference time.