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In this paper, we devote to the investigation of passivity in two types of coupled stochastic neural networks (CSNNs) with multiweights and incompatible input and output dimensions. First, some new definitions of passivity are proposed for stochastic systems that may have incompatible input and output dimensions. By utilizing stochastic analysis techniques and Lyapunov functional method, several sufficient conditions are respectively developed for ensuring that CSNNs without and with multiple delay couplings can realize passivity. Besides, the synchronization criteria for CSNNs with multiweights are established by employing the results of output-strictly passivity. Finally, two simulation examples are given to illustrate the validity of the theoretical results.