The paper introduces the Hidden Tree Markov Network (HTN), a neuro-probabilistic hybrid fusing the representation power of generative models for trees with the incremental and discriminative learning capabilities of neural networks. We put forward a modular architecture in which multiple generative models of limited complexity are trained to learn structural feature detectors whose outputs are then combined and integrated by neural layers at a later stage. In this respect, the model is both deep, thanks to the unfolding of the generative models on the input structures, as well as wide, given the potentially large number of generative modules that can be trained in parallel. Experimental results show that the proposed approach can outperform state-of-the-art syntactic kernels as well as generative kernels built on the same probabilistic model as the HTN.