This paper is concerned with distributed H_∞ filtering for a class of continuous-time linear plants over sensor networks with multiple communication channels (MCCs). A practical framework is presented to optimize communication over MCCs with uncertain delays and switching characteristics. The channel switching is assumed to follow a continuous-time Markov chain and a Markov jump linear system (MJLS) is exploited to model the overall networked system. A class of Lyapunov-Krasovskii functionals are constructed to derive sufficient conditions on stochastic stability and H_∞ performance of the MJLS in terms of linear matrix inequalities. Furthermore, the filtering parameter design is presented by employing Projection Lemma and LMI techniques.