Joint rendering and deformation of mesh and 3D Gaussian Splatting (3DGS) have significant value as both representations offer complementary advantages for graphics applications. However, due to differences in representation and rendering pipelines, existing studies render meshes and 3DGS separately, making it difficult to accurately handle occlusions and transparency. Moreover, the deformed 3DGS still suffers from visual artifacts due to the sensitivity to the topology quality of the proxy mesh. These issues pose serious obstacles to the joint use of 3DGS and meshes, making it difficult to adapt 3DGS to conventional mesh-oriented graphics pipelines. We propose UniMGS, the first unified framework for rasterizing mesh and 3DGS in a single-pass anti-aliased manner, with a novel binding strategy for 3DGS deformation based on proxy mesh. Our key insight is to blend the colors of both triangle and Gaussian fragments by anti-aliased α-blending in a single pass, achieving visually coherent results with precise handling of occlusion and transparency. To improve the visual appearance of the deformed 3DGS, our Gaussian-centric binding strategy employs a proxy mesh and spatially associates Gaussians with the mesh faces, significantly reducing rendering artifacts. With these two components, UniMGS enables the visualization and manipulation of 3D objects represented by mesh or 3DGS within a unified framework, opening up new possibilities in embodied AI, virtual reality, and gaming. We will release our source code to facilitate future research.