In this contribution we propose and study a novel multiuser detection (MUD) scheme for multicarrier direct-sequence code-division multiple-access systems employing both time (T)-domain and frequency (F)-domain spreading, which are referred to as the TF/MC DS-CDMA systems. Specifically, a reliability-aided MUD scheme is proposed, which consists of a linear MUD and a so-called L-level maximum-likelihood (ML)-MUD. The linear MUD is either a joint TF-domain linear MUD or constituted by two linear MUDs, one of which is operated in the T-domain and the other one in the F-domain. The L-level ML-MUD is a reduced ML-MUD, which only searches in a space of size 2 L in order to find the optimum solutions for the L most unreliable data bits detected by the linear MUD. In this contribution the bit error rate (BER) performance of the TF/MC DS-CDMA using the reliability-aided MUD is investigated, when communicating over additive white Gaussian noise (AWGN) channels or over frequency-selective Rayleigh fading channels. Our simulation results show that the reliability-aided MUD is capable of significantly outperforming the corresponding linear MUD. It can be shown that, provided that the signal-to-noise ratio (SNR) is sufficiently high, the reliability-aided MUD can readily obtain several decibels of SNR gain over the linear MUD at the cost of slight or moderate increase of the detection complexity.