Today's autonomous agents, largely driven by foundation models (FMs), can understand natural language instructions and solve long-horizon tasks with human-like reasoning. However, current human-robot interaction frameworks largely follow a one-way master-apprentice technique where the embodied agent passively executes commands without reciprocal learning. This neglects the co-adaptive, multi-turn nature of everyday human-to-human interactions. We introduce symbiotic interactive learning (SIL), a bidirectional co-adaptation framework in a shared latent task space, where both the human and the agent maintain joint belief states that evolve with the interaction history. This enables proactive clarification, adaptive suggestions, and shared plan refinement. SIL leverages FMs for spatial perception and reasoning, together with a triplet-loss-trained neural encoder that grounds the FMs' outputs into task-specific latent representations. To support long-term stability as tasks evolve, SIL utilises episodic and semantic memory architectures, regularised via elastic weight consolidation to mitigate catastrophic forgetting. We evaluate SIL on simulated and real-world embodied tasks, including instruction following, information retrieval, query-oriented reasoning, and interactive dialogue, achieving a $90.4\%$ task completion rate and a belief alignment score of $ρ\approx 0.83$, an absolute improvement of about $20$ percentage points over the best ablations. Demos and resources: https://linusnep.github.io/SIL/.