We propose Transmission-Reflection Gaussians (TR-Gaussians), a novel 3D-Gaussian-based representation for high-fidelity rendering of planar transmission and reflection, which are ubiquitous in indoor scenes. Our method combines 3D Gaussians with learnable reflection planes that explicitly model the glass planes with view-dependent reflectance strengths. Real scenes and transmission components are modeled by 3D Gaussians and the reflection components are modeled by the mirrored Gaussians with respect to the reflection plane. The transmission and reflection components are blended according to a Fresnel-based, view-dependent weighting scheme, allowing for faithful synthesis of complex appearance effects under varying viewpoints. To effectively optimize TR-Gaussians, we develop a multi-stage optimization framework incorporating color and geometry constraints and an opacity perturbation mechanism. Experiments on different datasets demonstrate that TR-Gaussians achieve real-time, high-fidelity novel view synthesis in scenes with planar transmission and reflection, and outperform state-of-the-art approaches both quantitatively and qualitatively.