Creating high-fidelity head avatars from multi-view videos is essential for many AR/VR applications. However, current methods often struggle to achieve high-quality renderings across all head components (e.g., skin vs. hair) due to the limitations of using one single representation for elements with varying characteristics. In this paper, we introduce a Hybrid Mesh-Gaussian Head Avatar (MeGA) that models different head components with more suitable representations. Specifically, we employ an enhanced FLAME mesh for the facial representation and predict a UV displacement map to provide per-vertex offsets for improved personalized geometric details. To achieve photorealistic rendering, we use deferred neural rendering to obtain facial colors and decompose neural textures into three meaningful parts. For hair modeling, we first build a static canonical hair using 3D Gaussian Splatting. A rigid transformation and an MLP-based deformation field are further applied to handle complex dynamic expressions. Combined with our occlusion-aware blending, MeGA generates higher-fidelity renderings for the whole head and naturally supports diverse downstream tasks. Experiments on the NeRSemble dataset validate the effectiveness of our designs, outperforming previous state-of-the-art methods and enabling versatile editing capabilities, including hairstyle alteration and texture editing.