This study concerns the problem of asynchronous H∞ filtering in relation to a class of two-dimensional (2D) Markov jump systems. The asynchronous phenomenon is considered to occur in a random way, and the mismatch behaviour is determined by a stochastic variable with Bernoulli random binary distribution. A stochastic parameter-dependent approach is proposed for the design of H∞ filter such that, for any admissible random mismatch, the filtering error system is mean-square asymptotically stable and has a prescribed H∞ performance level. Moreover, a key relationship of the H∞ performance between the results presented and the classical mode-dependent, mode-independent filtering is demonstrated. A numerical example is provided to illustrate the effectiveness and advantage of the developed theoretical results.