In this paper, we propose a widely-linear (WL) receiver structure for multiple access interference (MAI) and {jamming signal (JS)} suppression in direct-sequence code-division multiple-access (DS-CDMA) systems. A vector space projection (VSP) scheme is also considered to cancel the {JS} before detecting the desired signals. We develop a novel multiple-candidate successive interference cancellation (MC-SIC) scheme which processes two consecutive user symbols at one time to process the unreliable estimates and a number of selected points serve as the feedback candidates for interference cancellation, which is effective for alleviating the effect of error propagation in the SIC algorithm. Widely-linear signal processing is then used to enhance the performance of the receiver in non-circular modulation scheme. By bringing together the techniques mentioned above, a novel interference suppression scheme is proposed which combines the widely-linear multiple-candidate SIC (WL-MC-SIC) minimum mean-squared error (MMSE) algorithm with the VSP scheme to suppress MAI and {JS} simultaneously. Simulations for binary phase shift keying (BPSK) modulation scenarios show that the proposed structure achieves a better MAI suppression performance compared with previously reported SIC MMSE receivers at lower complexity and a superior {JS} suppression performance.