This paper is devoted to the robust dissipativity and passivity problems for Markovian switching complex-valued neural networks with probabilistic time-varying delay, where the transition rates are partly unknown, which might reflect more realistic dynamical behaviors of the switching networks. The probabilistic delay is described by a sequence of bernoulli distributed random variables, and mode-dependent parameter uncertainties are assumed to be norm-bounded. Based on the complex version of the generalized It$\hat{o}$’s formula, the robust analysis tools and the stochastic analysis methods, some sufficient mode/delay-dependent criteria on the $(M,N,W)$-dissipativity and passivity are derived in terms of complex matrix inequalities. In the end of paper, two numerical examples are presented to illustrate the effectiveness and feasibility of the obtained results.