This study is concerned with distributed H∞ filtering for continuous‐time linear systems over sensor networks with heterogeneous Markovian coupling intercommunication delays. The set of sensor nodes forms a sensing and communication network whose topology is modelled by a directed graph that describes the measurement exchanged among neighbouring sensor nodes. Heterogeneous random coupling delays modelled by a Markov process are considered in the intercommunication between interacting sensor nodes. A refined two‐step decoupling technique is presented to deal with the complicated coupling of exchanged measurement in the presence of the delays. A sufficient condition on the existence of desired distributed H∞ filters is derived such that the resultant filtering error system is mean square exponentially stable with prescribed weighting average H∞ performance. Two illustrative examples are given to show the effectiveness of the proposed results.