This paper is concerned with the distributed H∞ state estimation for a discrete-time target linear system over a filtering network with time-varying and switching topology and partial information exchange. Both filtering network topology switching and partial information exchange between filters are simultaneously considered in the filter design. The topology under consideration evolves not only over time but also by an event switch which is assumed to be subject to a nonhomogeneous Markov chain. The probability transition matrix of the nonhomogeneous Markov chain is time-varying. In the filter information exchange, partial state estimation information and channel noise are simultaneously considered. In order to design such a switching filtering network with partial information exchange, stochastic Markov stability theory is developed. The switching topology-dependent filters are derived to guarantee an optimal H∞ disturbance rejection attenuation level for the estimation disagreement of the filtering network. It is shown that the addressed H∞ state estimation problem is turned into a switching topology-dependent optimal problem. The distributed filtering problem with complete information exchanges from its neighbors is also investigated. An illustrative example is given to show the applicability of the obtained results.