Tropical dry forests and savannas provide important ecosystem services and harbor high biodiversity, yet are globally under pressure from land-use change. Mapping changes in the condition of dry forests and savannas is therefore critical. This can be challenging given that these ecosystems are characterized by continuous gradients of tree and shrub cover, resulting in considerable structural complexity. We developed a novel approach to map, separately, continuous fields of tree cover and shrub cover across the South American Gran Chaco (1,100,000 km2), making full use of the Landsat-8 optical and Sentinel-1 synthetic aperture radar (SAR) image archives. We gathered a large training dataset digitized from very-high resolution imagery and used a gradient-boosting framework to model continuous fields of tree cover and shrub cover at 30-m resolution. Our regression models had high to moderate predictive power (85.5% for tree cover, and 68.5% for shrub cover) and resulted in reliable tree and shrub cover maps (mean squared error of 4.4% and 6.4% for tree- and shrub cover respectively). Models jointly using optical and SAR imagery performed substantially better than models using single-sensor imagery, and model predictors differed strongly in some regions, especially in areas of dense vegetation cover. Mapping tree and shrub cover separately allowed identifying distinct vegetation formations, with shrub-dominated systems mainly in the very dry Chaco, woodlands with large trees mainly in the dry Chaco, and tree-dominated savannas in the wet Chaco. Our tree and shrub cover layers also revealed considerable edge effects in terms of woody cover away from agricultural fields (edge effects extending about 2 km), smallholder ranches (about 1.2 km), and roads and railways (about 1.4 and 0.9 km, respectively). Our analyses highlight both the substantial footprint of land-use on remaining natural vegetation in the Chaco, and the potential of multi-sensoral approaches to monitor forest degradation. More broadly, our approach shows that mapping canopy structure and distinct layers of woody vegetation in dry forest and savannas is possible across large areas, and highlights the value of the growing Landsat and Sentinel archives for doing so.