The H₂/H_∞  filtering for complex multi-channel networked systems with different network-related nondeterministic issues in each channel is studied, where multiple signals are encapsulated into single packet and transmitted through one common channel. By using a maximum data packet out-of-order strategy, multi-channel communication constraints from the sensor to the filter are firstly solved within one framework. A generalized comprehensive filtering error dynamic system model which contains multi-channel communication constraints is then established. Under the known maximum network-induced delays and the known number of data packet dropout, the designed filter enables multi-channel error dynamic system to be stochastic stability and to guarantee a prescribed H₂/H_∞ performance. Numerical simulation results show the feasibility and efficiency of the proposed method.