Due to the lack of effective cross-modal modeling, existing open-source audio-video generation methods often exhibit compromised lip synchronization and insufficient semantic consistency. To mitigate these drawbacks, we propose UniAVGen, a unified framework for joint audio and video generation. UniAVGen is anchored in a dual-branch joint synthesis architecture, incorporating two parallel Diffusion Transformers (DiTs) to build a cohesive cross-modal latent space. At its heart lies an Asymmetric Cross-Modal Interaction mechanism, which enables bidirectional, temporally aligned cross-attention, thus ensuring precise spatiotemporal synchronization and semantic consistency. Furthermore, this cross-modal interaction is augmented by a Face-Aware Modulation module, which dynamically prioritizes salient regions in the interaction process. To enhance generative fidelity during inference, we additionally introduce Modality-Aware Classifier-Free Guidance, a novel strategy that explicitly amplifies cross-modal correlation signals. Notably, UniAVGen's robust joint synthesis design enables seamless unification of pivotal audio-video tasks within a single model, such as joint audio-video generation and continuation, video-to-audio dubbing, and audio-driven video synthesis. Comprehensive experiments validate that, with far fewer training samples (1.3M vs. 30.1M), UniAVGen delivers overall advantages in audio-video synchronization, timbre consistency, and emotion consistency.