State-of-the-art music recommender systems are based on collaborative filtering, which builds upon learning similarities between users and songs from the available listening data. These approaches inherently face the cold-start problem, as they cannot recommend novel songs with no listening history. Content-aware recommendation addresses this issue by incorporating content information about the songs on top of collaborative filtering. However, methods falling in this category rely on a shallow user/item interaction that originates from a matrix factorization framework. In this work, we introduce neural content-aware collaborative filtering, a unified framework which alleviates these limits, and extends the recently introduced neural collaborative filtering to its content-aware counterpart. We propose a generative model which leverages deep learning for both extracting content information from low-level acoustic features and for modeling the interaction between users and songs embeddings. The deep content feature extractor can either directly predict the item embedding, or serve as a regularization prior, yielding two variants (strict and relaxed) of our model. Experimental results show that the proposed method reaches state-of-the-art results for a cold-start music recommendation task. We notably observe that exploiting deep neural networks for learning refined user/item interactions outperforms approaches using a more simple interaction model in a content-aware framework.