The growth of e-commerce has seen a surge in popularity of platforms like Amazon, eBay, and Taobao. This has given rise to a unique shopping behavior involving baskets - sets of items purchased together. As a less studied interaction mode in the community, the question of how should shopping basket complement personalized recommendation systems remains under-explored. While previous attempts focused on jointly modeling user purchases and baskets, the distinct semantic nature of these elements can introduce noise when directly integrated. This noise negatively impacts the model's performance, further exacerbated by significant noise (e.g., a user is misled to click an item or recognizes it as uninteresting after consuming it) within both user and basket behaviors. In order to cope with the above difficulties, we propose a novel Basket recommendation framework via Noise-tolerated Contrastive Learning, named BNCL, to handle the noise existing in the cross-behavior integration and within-behavior modeling. First, we represent the basket-item interactions as the hypergraph to model the complex basket behavior, where all items appearing in the same basket are treated as a single hyperedge. Second, cross-behavior contrastive learning is designed to suppress the noise during the fusion of diverse behaviors. Next, to further inhibit the within-behavior noise of the user and basket interactions, we propose to exploit invariant properties of the recommenders w.r.t augmentations through within-behavior contrastive learning. A novel consistency-aware augmentation approach is further designed to better identify the noisy interactions with the consideration of the above two types of interactions. Our framework BNCL offers a generic training paradigm that is applicable to different backbones. Extensive experiments on three shopping transaction datasets verify the effectiveness of our proposed method.