Hypergraph neural networks (HNNs) have emerged as powerful tools for modeling high-order relationships in complex systems. However, most existing HNNs are designed under the assumption of homophily, which does not hold in many real-world scenarios where connected nodes often exhibit diverse semantics, i.e., heterophily. This inconsistency leads to suboptimal aggregation and degraded performance, especially in low-label regimes. While a few recent methods have attempted to enhance heterophilic hypergraph learning, they often rely heavily on label supervision and overlook the potential of self-supervised techniques. In this paper, we propose HeroCL, a heterophily-aware contrastive learning framework that improves hypergraph representation under both structural heterogeneity and label scarcity. Specifically, HeroCL integrates a multi-hop neighbor encoding module to capture informative higher-order context and incorporates two complementary contrastive objectives, label-aware and structure-aware, to guide representation learning from both semantic and relational perspectives. A multi-granularity contrastive strategy is introduced to exploit latent signals across multiple neighborhood levels. Extensive experiments on several benchmark datasets against 11 existing baselines demonstrate that HeroCL achieves consistent and significant performance gains, particularly under strong heterophily and limited supervision, validating its robustness and effectiveness.