Capturing users' precise preferences is of great importance in various recommender systems (e.g., e-commerce platforms and online advertising sites), which is the basis of how to present personalized interesting product lists to individual users. In spite of significant progress has been made to consider relations between users and items, most of existing recommendation techniques solely focus on singular type of user-item interactions. However, user-item interactive behavior is often exhibited with multi-type (e.g., page view, add-to-favorite and purchase) and inter-dependent in nature. The overlook of multiplex behavior relations can hardly recognize the multi-modal contextual signals across different types of interactions, which limit the feasibility of current recommendation methods. To tackle the above challenge, this work proposes a Memory-Augmented Transformer Networks (MATN), to enable the recommendation with multiplex behavioral relational information, and joint modeling of type-specific behavioral context and type-wise behavior inter-dependencies, in a fully automatic manner. In our MATN framework, we first develop a transformer-based multi-behavior relation encoder, to make the learned interaction representations be reflective of the cross-type behavior relations. Furthermore, a memory attention network is proposed to supercharge MATN capturing the contextual signals of different types of behavior into the category-specific latent embedding space. Finally, a cross-behavior aggregation component is introduced to promote the comprehensive collaboration across type-aware interaction behavior representations, and discriminate their inherent contributions in assisting recommendations. Extensive experiments on two benchmark datasets and a real-world e-commence user behavior data demonstrate significant improvements obtained by MATN over baselines. Codes are available at: https://github.com/akaxlh/MATN.