A multi-channel model, describing the effects of spectral and temporal integration in amplitude-modulation detection for a stochastic noise carrier, is proposed and validated. The model is based on the modulation filterbank concept which was established in the accompanying paper [Dau et al., J. Acoust. Soc. Am. 102, 2892-2905 (1997)] for modulation perception in narrow-band conditions (single-channel model). To integrate information across frequency, the detection process of the model linearly combines the channel outputs. To integrate information across time, a kind of "multiple-look" strategy, is realized within the detection stage of the model. Both data from the literature and new data are used to validate the model. The model predictions agree with the results of Eddins [J. Acoust. Soc. Am. 93, 470-479 (1993)] that the "time constants" associated with the temporal modulation transfer functions (TMTF) derived for narrow-band stimuli do not vary with carrier frequency region and that they decrease monotonically with increasing stimulus bandwidth. The model is able to predict masking patterns in the modulation-frequency domain, as observed experimentally by Houtgast [J. Acoust. Soc. Am. 85, 1676-1680 (1989)]. The model also accounts for the finding by Sheft and Yost [J. Acoust. Soc. Am. 88, 796-805 (1990)] that the long "effective" integration time constants derived from the data are two orders of magnitude larger than the time constants derived from the cutoff frequency of the TMTF. Finally, the temporal-summation properties of the model allow the prediction of data in a specific temporal paradigm used earlier by Viemeister and Wakefield [J. Acoust. Soc. Am. 90, 858-865 (1991)]. The combination of the modulation filterbank concept and the optimal decision algorithm proposed here appears to present a powerful strategy for describing modulation-detection phenomena in narrow-band and broadband conditions.