This article investigates the asynchronous distributed finite-time H∞ filtering problem for nonlinear Markov jump systems over sensor networks under stochastic attacks. The stochastic attacks, called two-channel deception attacks, exist not only between the Markov jump plant and the sensors but also among the sensors. It is assumed that the mode of the filter relies on, but is asynchronous with, that of the Markov jump plant. First, we establish a filtering error system that combines the Markov jump plant with the asynchronous filtering system. Then, we present an asynchronous distributed filter, which ensures the filtering error system mean-square finite-time bounded and satisfies a prescribed H∞ performance level under the two-channel attacks. Finally, an example is given to illustrate the effectiveness of the presented filter.