This paper investigates the asymmetric connectedness between global banks and insurance companies under varying market conditions, with a particular focus on tail risk transmission. Motivated by the growing integration between banking and insurance sectors, we move beyond traditional average-based models and adopt a quantile vector autoregression (QVAR) framework to capture nonlinear spillovers across the 5th, 50th, and 95th percentiles of daily return distributions (2016–2025). Our analysis reveals three key findings: (1) Total connectedness intensifies sharply during both distress and exuberance, highlighting strong state dependence in systemic risk; (2) banks consistently act as net receivers of shocks at both tails, whereas certain insurers, particularly those with broader financial exposure, emerge as persistent net transmitters; and (3) connectedness in the tails is largely symmetric, though marginally stronger during downturns, underscoring heightened vulnerability in periods of stress. These findings emphasise the limitations of mean-based approaches and reinforce the value of tail-sensitive models for capturing regime shifts in financial contagion. The framework offers a replicable, data-driven approach to systemic risk monitoring that is especially relevant for SEACEN member economies aiming to strengthen macroprudential surveillance in the face of increasingly complex cross-sector linkages.