Current audio-driven 3D head generation methods mainly focus on single-speaker scenarios, lacking natural, bidirectional listen-and-speak interaction. Achieving seamless conversational behavior, where speaking and listening states transition fluidly remains a key challenge. Existing 3D conversational avatar approaches rely on error-prone pseudo-3D labels that fail to capture fine-grained facial dynamics. To address these limitations, we introduce a novel two-stage framework MANGO, which leveraging pure image-level supervision by alternately training to mitigate the noise introduced by pseudo-3D labels, thereby achieving better alignment with real-world conversational behaviors. Specifically, in the first stage, a diffusion-based transformer with a dual-audio interaction module models natural 3D motion from multi-speaker audio. In the second stage, we use a fast 3D Gaussian Renderer to generate high-fidelity images and provide 2D-level photometric supervision for the 3D motions through alternate training. Additionally, we introduce MANGO-Dialog, a high-quality dataset with over 50 hours of aligned 2D-3D conversational data across 500+ identities. Extensive experiments demonstrate that our method achieves exceptional accuracy and realism in modeling two-person 3D dialogue motion, significantly advancing the fidelity and controllability of audio-driven talking heads.