The phenomenon of stochastic resonance (SR) in a mono-threshold-system-based detector (MTD) with additive background noise and multiplicative external noise is investigated. On the basis of maximum a posteriori probability (MAP) criterion, we deal with the binary signal transmission in four scenarios. The performance of the MTD is characterized by the probability of error detection, and the effects of system threshold and noise intensity on detectability are discussed in this paper. Similar to prior studies that focus on additive noises, along with increases in noise intensity, we also observe a non-monotone phenomenon in the multiplicative ways. However, unlike the case with the additive noise, optimal multiplicative noises all tend toward infinity for fixed additive noise intensities. The results of our model are potentially useful for the design of a sensor network and can help one to understand the biological mechanism of synaptic transmission.