The dependencies between system and user utterances in the same turn and across different turns are not fully considered in existing multidomain dialogue state tracking (MDST) models. In this study, we argue that the incorporation of these dependencies is crucial for the design of MDST and propose Parallel Interactive Networks (PIN) to model these dependencies. Specifically, we integrate an interactive encoder to jointly model the in-turn dependencies and cross-turn dependencies. The slot-level context is introduced to extract more expressive features for different slots. And a distributed copy mechanism is utilized to selectively copy words from historical system utterances or historical user utterances. Empirical studies demonstrated the superiority of the proposed PIN model.