This article establishes a method for deriving the spectral representation of an inherently Markov-switching bilinear process. The procedure is based on the application of the Riesz-Fisher theorem, which states that the spectral density can be obtained as the Fourier transform of the covariance function. We provide sufficient conditions for the second-order stationarity of models, expressed in terms of the spectral radius of a specific matrix that involves the model’s coefficients. The exact form of the spectral density function demonstrates that it is impossible to distinguish between an and an model solely based on the second-order properties of the process.