This paper is concerned with the distributed H-infinity-consensus filtering problem for a class of discrete time-varying systems with stochastic nonlinearities and multiple missing measurements. The stochastic nonlinearities are formulated by statistical means and the missing measurements are characterized by a set of random variables obeying Bernoulli distribution. A novel H-infinity-consensus performance index is proposed to measure both the filtering accuracy of every node and the consensus among neighbor nodes. Then, a new concept called stochastic vector dissipativity is proposed wherein the dissipation matrix is formulated by a nonsingular substochastic matrix, which is skillfully constructed by a new defined interval function on the out-degree. A set of local sufficient conditions in terms of the recursive linear matrix inequalities is presented for each node such that the proposed H-infinity-consensus performance can be guaranteed for the local augmented dynamics over the finite horizon. Furthermore, a novel algorithm proposed here can be implemented on each node. Finally, an illustrative simulation is presented to demonstrate the effectiveness and applicability of the proposed algorithm.