Indigenous forests cover 24% of New Zealand and provide valuable ecosystem services. However, a national map of forest types, that is, physiognomic types, which would benefit conservation management, does not currently exist at an appropriate level of detail. While traditional forest classification approaches from remote sensing data are based on spectral information alone, the joint use of space-based optical imagery and structural information from synthetic aperture radar (SAR) and canopy metrics from air-borne Light Detection and Ranging (LiDAR) facilitates more detailed and accurate classifications of forest structure. We present a support vector machine (SVM) classification using data from ESA’s Sentinel-1 and 2 missions, ALOS PALSAR, and airborne LiDAR to produce a regional map of physiognomic types of indigenous forest in New Zealand. A five-fold cross-validation of ground data showed that the highest classification accuracy of 80.9% is achieved for bands 2, 3, 4, 5, 8, 11, and 12 from Sentinel-2, the ratio of bands VH and VV from Sentinel-1, HH from PALSAR, and mean canopy height and 97th percentile canopy height from LiDAR. The classification based on the optical bands alone was 73.1% accurate and the addition of structural metrics from SAR and LiDAR increased accuracy by 7.8%. The classification accuracy is sufficient for many management applications for indigenous forest in New Zealand, including biodiversity management, carbon inventory, pest control, ungulate management, and disease management. National application of the method will be possible in several years, once national LiDAR coverage is achieved, and a national canopy height model is available.