Recovering detailed interactions between humans/hands and objects is an appealing yet challenging task. Existing methods typically use template-based representations to track human/hand and objects in interactions. Despite the progress, they fail to handle the invisible contact surfaces. In this paper, we propose Ins-HOI, an end-to-end solution to recover human/hand-object reconstruction via instance-level implicit reconstruction. To this end, we introduce an instance-level occupancy field to support simultaneous human/hand and object representation, and a complementary training strategy to handle the lack of instance-level ground truths. Such a representation enables learning a contact prior implicitly from sparse observations. During the complementary training, we augment the real-captured data with synthesized data by randomly composing individual scans of humans/hands and objects and intentionally allowing for penetration. In this way, our network learns to recover individual shapes as completely as possible from the synthesized data, while being aware of the contact constraints and overall reasonability based on real-captured scans. As demonstrated in experiments, our method Ins-HOI can produce reasonable and realistic non-visible contact surfaces even in cases of extremely close interaction. To facilitate the research of this task, we collect a large-scale, high-fidelity 3D scan dataset, including 5.2k high-quality scans with real-world human-chair and hand-object interactions. We will release our dataset and source codes. Data examples and the video results of our method can be found on the project page.