Operational canopy height mapping at high resolution remains a challenging task at country- level. Most of the existing state-of-the-art inversion methods propose physically-based schemes which are specifically tuned for local scales. Only few approaches in the literature have attempted to produce country or global scale estimates, mostly by means of data-driven approaches and multi-spectral data sources. In this paper, we propose a robust deep learning approach that exploits single-pass interferometric TanDEM-X data to generate accurate forest height estimates from a single interferometric bistatic acquisition. The model development is driven by considerations on both the final performance and the trustworthiness of the model for large-scale deployment in the context of tropical forests. We train and test our model over the five tropical sites of the AfriSAR 2016 campaign, situated in the West Central state of Gabon, performing spatial cross-validation experiments to test its generalization capability. We define a specific training dataset and input predictors to develop a robust model for country-scale inference, by finding an optimal trade-off between the model performance and the large-scale reliability. The proposed model achieves an overall estimation bias of 0.12 m, a mean absolute error of 3.90 m, a root mean squared error of 5.08 m and a coefficient of determination of 0.77. Finally, we generate a time-tagged country-scale canopy height map of Gabon at 25 m resolution, discussing the potential and challenges of these kinds of products for their application in different scenarios and for the monitoring of forest changes.