This paper presents a machine learning based method to predict the forest structure parameters from L-band polarimetric and interferometric synthetic aperture radar (PolInSAR) data acquired by the airborne UAVSAR system over the Réserve Faunique des Laurentides in Québec, Canada. The main objective of this paper is to show that relevant parameters of the PolInSAR coherence region can be used to invert forest structure indicators computed from the airborne LIDAR sensor Laser Vegetation and Ice Sensor (LVIS). The method relies on the shape of the observed generalized PolInSAR coherence region that is related to the three-dimensional structure of the scene. In addition to parameters describing the coherence shape, we consider the impact of acquisition parameters such as the interferometric baseline, ground elevation and local surface slope. We use the parameters as input a multilayer perceptron model to infer canopy features as estimated from LIDAR waveform. The output features are canopy height, cover and vertical profile class. Canopy height and canopy cover are estimated with a normalized RMSE of 13%, 15% respectively. The vertical profile was divided into 3 distinct classes with 66% accuracy.