Multi-behavior graph recommendation systems can simultaneously consider various user behaviors on the platform, such as clicks, purchases, comments, etc., thus more comprehensively capturing user behavior patterns and preferences and handling heterogeneous relationships. Despite achieving commendable results, recommender systems based on hypergraphs still face challenges. Firstly, the effectiveness of Collaborative Filtering(CF) is affected when encountering real-world data with skewed distributions. Secondly, large-scale auxiliary behaviors contain a lot of noise. In order to address these issues, we propose a novel recommendation framework Multi-behavior Heterogeneous Hypergraph Contrastive Recommendation (MHHCR), including hypergraph global dependency learning and contrastive learning tasks to solve above challenges, respectively. Extensive experiments demonstrate that the effectiveness of MHHCR on two real-world datasets, achieving SOTA performance over various state-of-the-art baselines. Source code is available at https://github.com/Anticoder1/MHHCR-rec .