Digital printing has focused on multilevel dithering using a stochastic screen as this procedure is simple to implement and yields a smooth output pattern. In bilevel halftoning with a stochastic screen, two printable output levels, i.e., black and white, corresponding to the input image, values are determined by the threshold values of the stochastic screen. For multilevel halftoning, these threshold values are then simply extended using a scaling function. Yet, a simple extension using a scaling function also generates banding artifacts around the intermediate printable tone levels, producing discontinuity in a smooth tone transition region. Therefore, to reduce these banding artifacts, this article proposes blue-noise multilevel dithering with interweaving dot dispersion. First, to investigate the cause and characteristics of the banding artifacts, multilevel halftoning using a simple scaling function is analyzed using a probability model when varying the number of tone levels, thereby generalizing the characteristics of the banding artifacts. The scaling function for the multilevel halftoning is then modified using two control factors based on the generalized characteristics of the banding artifacts according to the number of printable tone levels in order to interweave dot dispersion in the banding regions. The dot distribution across the banding regions is affected by the two control factors that control the interweaving point. The specific values for the control factors are determined by investigating via subjective observation and the human visual system weighted root mean squared error (HVS-WRMSE) curve using the perceived root mean square and based on characteristics of the human visual system. In experiments, an objective evaluation using the HVS-WRMSE of a multitoned image is used to compare the quality of the multitoned patterns around the intermediate tone levels. The proposed method is found to moderately reduce the banding artifacts in the gray ramp when compared to the conventional methods.