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With an increasing penetration level of intermittent renewable energy sources and heterogeneous energy demands, the secure and economic operation of multi-energy microgrids (MEMGs) becomes more and more critical. Under this circumstance, this paper proposes an adaptive (two-layer) stochastic approach to obtain optimal MEMG operation decisions by taking advantage of distinct energy properties. First, rather than merely focusing on the active power economic dispatch, voltage/var control (VVC) scheme is involved to co-optimize the active and reactive power flow while guaranteeing voltage security; Second, a battery degradation model and a comprehensive thermal network model with thermal energy flow and transmission delay are presented to derive practical and efficient operations; Third, a conditional value-at-risk (CVaR)-based risk evaluation method is included to avoid over-optimistic solutions …