This paper proposes an online algorithm for energy storage management in networked microgrids (MGs) with co-generation based on the concept of quality-of-service in electricity (QoSE). The concept of networked MG with distributed renewable energy supply and co-generation makes power supply smarter for electricity/heat using, which has advantages of increasing power supply efficiency and reliability by coordinately scheduling the power supply in a networked way. The demands include quality usage of electricity load and heat. The networked MG central controller aims to minimize the operation cost and guarantee the outage probability of quality usage, i.e., QoSE, by scheduling electricity among renewable energy sources, energy storage systems, co-generation, and external utility market. We formulate the problem as a stochastic programming problem with QoSE and battery capacity constraints. By introducing the QoSE virtual queues and energy storage virtual queues, we transform the original problem into a problem that is applicable to employ the Lyapunov optimization technique. The proposed algorithm is an online algorithm with low complexity for practical implementation, and also provides several deterministic performance bounds. We perform extensive simulations to demonstrate the effectiveness of the proposed algorithm, which exhibits significant efficiency on operation cost reduction compared with an alternative benchmark solution.