Generating talking avatars is a fundamental task in video generation. Although existing methods can generate full-body talking avatars with simple human motion, extending this task to grounded human-object interaction (GHOI) remains an open challenge, requiring the avatar to perform text-aligned interactions with surrounding objects. This challenge stems from the need for environmental perception and the control-quality dilemma in GHOI generation. To address this, we propose a novel dual-stream framework, InteractAvatar, which decouples perception and planning from video synthesis for grounded human-object interaction. Leveraging detection to enhance environmental perception, we introduce a Perception and Interaction Module (PIM) to generate text-aligned interaction motions. Additionally, an Audio-Interaction Aware Generation Module (AIM) is proposed to synthesize vivid talking avatars performing object interactions. With a specially designed motion-to-video aligner, PIM and AIM share a similar network structure and enable parallel co-generation of motions and plausible videos, effectively mitigating the control-quality dilemma. Finally, we establish a benchmark, GroundedInter, for evaluating GHOI video generation. Extensive experiments and comparisons demonstrate the effectiveness of our method in generating grounded human-object interactions for talking avatars. Project page: https://interactavatar.github.io