This work devotes to the event-based mixed H-infinity and passive filter analysis and design problems of discrete-time singular stochastic network systems with Markovian jump parameters. Using the event-triggered communication approach, we first derive a network-induced delay discrete error singular stochastic network model. With the help of event-triggered method and stochastic Lyapunov function scheme, sufficient conditions are then established such that the resulting error stochastic model is regular, causal, stochastically mean-square stable with a mixed H-infinity and passivity performance index. By applying slack matrix variables and filter transfer function equivalent method, an event-triggered mixed H-infinity and passive filter is designed such that the resulting error singular stochastic network system satisfies certain mixed H-infinity and passive filter performance index, and the derived conditions could be solved in terms of linear matrix inequality method. Finally, the effectiveness of the proposed methods is illustrated by a numerical example.