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This paper deals with the globally exponential stability of impulsive bidirectional associative memory (BAM) neural networks with both Markovian jump parameters and mixed time delays. The jumping parameters are determined by a continuous-time, discrete-state Markov chain. Different from the previous literature, the mixed time delays considered here comprise discrete, distributed and leakage time-varying delays. By using the Lyapunov–Krasovskii functional having triple integral terms and model transformation technique, some novel sufficient delay-dependent conditions are derived to ensure the globally exponential stability in the mean square of the suggested system. Moreover, the derivatives of time delays are not necessarily zero or smaller than one since several free matrices are introduced in our results. Finally, a numerical example and its simulations are provided to demonstrate the effectiveness of the theoretical results.