The cache-enabled multicast content pushing, which multicasts the content items to multiple users and caches them until requested, is a promising technique to alleviate the heavy network load by enhancing the traffic offloading. This, in turn, has called for the optimization of content pushing strategy while considering both the transmission and caching resources, which jointly result in the complicated coupling among pushing decisions and lead to high computational complexity. Unlike most existing approaches which simplify the pushing problem via bypassing the complicated coupling, in this paper, we propose a multicast content pushing strategy to maximize the offloaded traffic with the cost on content caching based on structured deep learning. Specifically, we design the convolution stage to extract the spatio-temporal correlations of one content item between different pushing decisions, and construct the fully-connected stage to capture the spatial coupling among the decisions of pushing different content items to different user devices. Moreover, to address the absence of the ground truth on multicast content pushing, we relax the transmission constraint to derive a performance upper bound for guiding the training direction. This relaxed problem is solved based on dynamic programming in a bottom-up manner. Compared to the state-of-the-art baselines including both the traditional model-based and the general neural network-based strategies, the proposed pushing strategy achieves significant performance gain in both the random-generated dataset and the real LastFM dataset. In addition, it is also shown that the proposed strategy is robust to the uncertainty of user request information.