This paper explores the chance-constrained set-membership filtering problem for complex networks subject to missing measurements and long-distance transmissions. To enhance the transmission reliability, a full-duplex relay was placed between the sensor and the remote filter, supplemented by a self-interference suppression mechanism to mitigate relay-induced disturbances. Missing measurements were modeled using Bernoulli random variables, while transmission uncertainties arising from long-distance transmission were characterized by stochastic channel parameters. The primary objective was to construct a filter that confines the filtering error within a predefined ellipsoidal bound at a specified probability level. To this end, sufficient conditions in the form of recursive linear matrix inequalities were derived, from which the corresponding filter gains were obtained. Within this framework, two optimization schemes were further formulated to achieve locally optimal filtering performance. A numerical result validated the effectiveness of the proposed method.