Long-context conversational agents require robust memory, but existing frameworks struggle to organize information effectively across dimensions like time and topic, leading to poor retrieval. To address this, we introduce H-Mem, a novel Hybrid Multi-Dimensional Memory architecture. H-Mem stores conversational facts in two parallel, hierarchical data structures: a temporal tree that organizes information chronologically and a semantic tree that organizes it conceptually. This dual-tree design enables a hybrid retrieval mechanism managed by an intelligent Mode Controller. Based on the query, the controller dynamically chooses between a sequential search using semantic anchors and an intersective search combining both hierarchies. Our experiments on long-context QA datasets demonstrate that H-Mem provides a more flexible approach to memory management, leading to significant improvements of over 8.4% compared to other state-of-the-art systems.