The stochastic resonance phenomenon in a bias linear system subject to multiplicative and additive dichotomous noise is investigated. From linear-response theory and the properties of the dichotomous noise, the exact expressions have been found for the first two moments and the signal-to-noise ratio (SNR). It is shown that the SNR is a non-monotonic function of the correlation time of the additive dichotomous noise, and varies non-monotonically with the bias of the external field and with the intensity and asymmetry of the multiplicative dichotomous noise, as with the external field frequency. Moreover, the SNR depends on the bias of the system and on the intensity of the cross noise between the multiplicative and additive dichotomous noise, as well as on the strength and asymmetry of the additive dichotomous noise.