Humanoid robotics has strong potential to transform daily service and caregiving applications. Although recent advances in general motion tracking within physics engines (GMT) have enabled virtual characters and humanoid robots to reproduce a broad range of human motions, these behaviors are primarily limited to contact-less social interactions or isolated movements. Assistive scenarios, by contrast, require continuous awareness of a human partner and rapid adaptation to their evolving posture and dynamics. In this paper, we formulate the imitation of closely interacting, force-exchanging human-human motion sequences as a multi-agent reinforcement learning problem. We jointly train partner-aware policies for both the supporter (assistant) agent and the recipient agent in a physics simulator to track assistive motion references. To make this problem tractable, we introduce a partner policies initialization scheme that transfers priors from single-human motion-tracking controllers, greatly improving exploration. We further propose dynamic reference retargeting and contact-promoting reward, which adapt the assistant's reference motion to the recipient's real-time pose and encourage physically meaningful support. We show that AssistMimic is the first method capable of successfully tracking assistive interaction motions on established benchmarks, demonstrating the benefits of a multi-agent RL formulation for physically grounded and socially aware humanoid control.