Multiple-access interference (MAI) limits the bit error rate (BER) performance of CDMA uplink transmission. In this paper, we propose a generalized chip-interleaved CDMA with 2-dimensional (2D) spreading using orthogonal variable spreading factor (OVSF) codes to minimize the MAI effects and achieve the maximum available time-and frequency-domain diversity gains. We present the code assignment for 2D spreading to provide users with flexible multi-rate data transmission. A computer simulation shows that by the joint use of 2D OVSF spreading and chip-interleaving, MAI-free transmission is possible for the quasi-synchronous DS- or MC-CDMA uplink, and hence the single-user frequency-domain equalization based on the MMSE criterion can be applied for signal detection. The BER performance in a time- and frequency-selective fading multiuser channel is theoretically analyzed and evaluated by both numerical computation and computer simulation.