Predicting the next interaction of a short-term sequence is a challenging task in session-based recommendation (SBR).Multi-behavior session recommendation considers session sequence with multiple interaction types, such as click and purchase, to capture more effective user intention representation sufficiently.Despite the superior performance of existing multi-behavior based methods for SBR, there are still several severe limitations:(i) Almost all existing works concentrate on single target type of next behavior and fail to model multiplex behavior sessions uniformly.(ii) Previous methods also ignore the semantic relations between various next behavior and historical behavior sequence, which are significant signals to obtain current latent intention for SBR.(iii) The global cross-session item-item graph established by some existing models may incorporate semantics and context level noise for multi-behavior session-based recommendation. To overcome the limitations (i) and (ii), we propose two novel tasks for SBR, which require the incorporation of both historical behaviors and next behaviors into unified multi-behavior recommendation modeling. To this end, we design a Multi-behavior Graph Contextual Aware Network (MGCNet) for multi-behavior session-based recommendation for the two proposed tasks. Specifically, we build a multi-behavior global item transition graph based on all sessions involving all interaction types. Based on the global graph, MGCNet attaches the global interest representation to final item representation based on local contextual intention to address the limitation (iii). In the end, we utilize the next behavior information explicitly to guide the learning of general interest and current intention for SBR. Experiments on three public benchmark datasets show that MGCNet can outperform state-of-the-art models for multi-behavior session-based recommendation.