The phenomenon of stochastic resonance (SR) in a bistable system subject to correlated multiplicative colored and additive white noises and a periodic rectangular signal with a constant component is investigated in the unified colored noise approximation and by applying the two-state theory. The expression of the signal-to-noise ratio (SNR) is obtained for arbitrary signal amplitude. The SNR is a non-monotonic function of intensities of multiplicative colored and additive white noises，correlation time of multiplicative colored noise and the strength of the coupling between noises， so SR appears in the bistable system. Meanwhile， it is more effective to control SR through adjusting the additive white noise intensity than adjusting the multiplicative colored noise intensity. Moreover，the effects of potential asymmetry and the strength of the coupling between noises on SNR are opposite.