The presence of both multiple-access interference (MAI) and intersymbol interference (ISI) constitutes a major impediment to reliable communications in multipath CDMA channels. An iterative receiver structure is proposed for decoding multiuser information data in a convolutionally coded asynchronous multipath DS-CDMA system. The receiver performs two successive soft-output decisions, achieved by a soft-input soft-output (SISO) multiuser detector and a bank of single-user SISO channel decoders, through an iterative process. A low-complexity SISO multiuser detector is developed based on a novel nonlinear interference suppression technique, which makes use of both soft-interference cancellation and linear MMSE filtering. Simulation results demonstrate that the proposed receiver offers significant performance gain over the traditional non-iterative receiver structure. Moreover, at high SNR, the detrimental effects of MAI and ISI can be almost completely overcome by iterative processing, and single-user performance can be approached.