Maps are crucial for various smart city applications as a core component of city geographic information systems (GIS). Developing effective Map Entity Representation Learning methods can extract semantic information for downstream tasks like crime rate prediction and land use classification, with significant application potential. A map comprises three entity types: land parcels, road segments, and points of interest. Most existing methods focus on a single entity type, losing inter-entity relationships and weakening representation effectiveness for real-world applications. Thus, jointly modelling and representing multiple map entity types is essential. However, designing a unified framework is challenging due to map data's unstructured, complex, and heterogeneous nature. We propose a novel method, HygMap, to represent all map entity types. We model the map as a heterogeneous hypergraph, design an encoder for map entities, and introduce a hybrid self-supervised training scheme. This architecture comprehensively captures the heterogeneous relationships among map entities at different levels. Experiments on nine downstream tasks with two real-world datasets show that our framework outperforms all baselines, with good computational efficiency and scalability.