Disentangled representation learning has recently attracted a significant amount of attention, particularly in the field of image representation learning. However, learning the disentangled representations behind a graph remains largely unexplored, especially for the attributed graph with both node and edge features. Disentanglement learning for graph generation has substantial new challenges including 1) the lack of graph deconvolution operations to jointly decode node and edge attributes; and 2) the difficulty in enforcing the disentanglement among latent factors that respectively influence: i) only nodes, ii) only edges, and iii) joint patterns between them. To address these challenges, we propose a new disentanglement enhancement framework for deep generative models for attributed graphs. In particular, a novel variational objective is proposed to disentangle the above three types of latent factors, with novel architecture for node and edge deconvolutions. Qualitative and quantitative experiments on both synthetic and real-world datasets demonstrate the effectiveness of the proposed model and its extensions.