In the past, our proposed HCoP-B has achieved route optimization and resolved the RO-storm problem for handoffs of the nested mobile network. However, because HCoP-B is a pure layer three, i.e., network layer, approach which handoff operations are performed after the layer two, i.e., data link layer, link breaks, it still suffers from a long handoff latency and serious packet losses. In this paper, by adopting the handoff prediction concept of the fast mobile IPv6 on HCoP-B, our cross-layer architecture, which is called the fast HCoP-B (FHCoP-B), can trigger HCoP-B layer three route optimization flow by 802.11 and 802.16 link events before the actual Layer 2 handoff occurs. In this way, FHCoP-B further shortens both the handoff latency and packet losses of HCoP-B.