Recent advancements in recommender systems have focused on integrating knowledge graphs (KGs) to leverage their auxiliary information. The core idea of KG-enhanced recommenders is to incorporate rich semantic information for more accurate recommendations. However, two main challenges persist: i) Neglecting complex higher-order interactions in the KG-based user-item network, potentially leading to sub-optimal recommendations, and ii) Dealing with the heterogeneous modalities of input sources, such as user-item bipartite graphs and KGs, which may introduce noise and inaccuracies. To address these issues, we present a novel Knowledge-enhanced Heterogeneous Hypergraph Recommender System (KHGRec). KHGRec captures group-wise characteristics of both the interaction network and the KG, modeling complex connections in the KG. Using a collaborative knowledge heterogeneous hypergraph (CKHG), it employs two hypergraph encoders to model group-wise interdependencies and ensure explainability. Additionally, it fuses signals from the input graphs with cross-view self-supervised learning and attention mechanisms. Extensive experiments on four real-world datasets show our model's superiority over various state-of-the-art baselines, with an average 5.18% relative improvement. Additional tests on noise resilience, missing data, and cold-start problems demonstrate the robustness of our KHGRec framework. Our model and evaluation datasets are publicly available at https://github.com/viethungvu1998/KHGRec.