The system under study is a convolutionally coded and orthogonally modulated DS-CDMA system over time-varying frequency-selective Rayleigh fading channels in multiuser environments. Iterative soft demodulation and decoding using the Turbo principle can be applied to such a system to increase the system capacity and performance. To combat multiple access interference (MAI), we incorporate the interference cancellation (IC) and decision-directed channel estimation (CE) in the demodulator. However, both IC and CE are subject to performance degradation due to incorrect decisions. In order to prevent error propagation from the decision feedback, soft interference cancellation and channel estimation assisted demodulation is proposed in this paper. The performance of this strategy is evaluated numerically and proved to be superior to the hard decision-directed approach with a minor increase in complexity.