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This paper proposes a unified approach to joint adaptive parameter estimation and interference cancellation (IC) for direct sequence code-division-multiple-access (DS-CDMA) systems in multipath channels. A unified framework is presented in which the IC problem is formulated as an optimization problem with extra degrees of freedom of an IC parameter vector for each stage and user. We propose a joint optimization method for estimating the IC parameter vector, the linear receiver filter front-end, and the channel along with minimum mean squared error (MMSE) expressions for the estimators. Based on the proposed joint optimization approach, we derive low-complexity stochastic gradient (SG) algorithms for estimating the desired parameters. Simulation results for the uplink of a synchronous DS-CDMA system show that the proposed methods significantly outperform the best known IC receivers.