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Systems subjected to switching random excitations are practically significant because they include many safety-critical systems such as power plants and communication networks. In this paper, the reliability of multi-degree, nonlinear, non-integrable Hamiltonian systems subjected to switching random excitations is investigated. Such a system is formulated as a continuous–discrete hybrid based upon the Markov jump theory. Stochastic averaging is applied to suppress the rapidly varying parameters of the Markov jump process in order to generate a probability-weighted diffusion equation. The associated backward Kolmogorov equation is then set up, from which the approximate reliability function and probability density of first passage time are obtained. The utility and accuracy of this approximate procedure are demonstrated by two examples.