Modern recommender systems often deal with a variety of user interactions, e.g., click, forward, purchase, etc., which requires the underlying recommender engines to fully understand and leverage multi-behavior data from users. Despite recent efforts towards making use of heterogeneous data, multi-behavior recommendation still faces great challenges. Firstly, sparse target signals and noisy auxiliary interactions remain an issue. Secondly, existing methods utilizing self-supervised learning (SSL) to tackle the data sparsity neglect the serious optimization imbalance between the SSL task and the target task. Hence, we propose a Multi-Behavior Self-Supervised Learning (MBSSL) framework together with an adaptive optimization method. Specifically, we devise a behavior-aware graph neural network incorporating the self-attention mechanism to capture behavior multiplicity and dependencies. To increase the robustness to data sparsity under the target behavior and noisy interactions from auxiliary behaviors, we propose a novel self-supervised learning paradigm to conduct node self-discrimination at both inter-behavior and intra-behavior levels. In addition, we develop a customized optimization strategy through hybrid manipulation on gradients to adaptively balance the self-supervised learning task and the main supervised recommendation task. Extensive experiments on five real-world datasets demonstrate the consistent improvements obtained by MBSSL over ten state-of-the art (SOTA) baselines. We release our model implementation at: https://github.com/Scofield666/MBSSL.git.