In this article, we focus on the cooperative multi-user network model and propose a relay-assisted partial packet recovery scheme in which asynchronous interleave-division multiple-access (IDMA) with iterative chip-by-chip multiuser detection (MUD) is used for the recovery of partial packets from multiple sources. In packet transmission, only a few erroneous bits may cause the entire packet to be discarded and partial packet recovery can reduce waste in resource by retransmitting only the bits that are unreliable, As the retransmitted partial packets for different sources can be of different lengths, IDMA is particularly suitable because of the simplicity of chip-by-chip MUD and because there is no need for strict synchronization. Our detailed scheme, which includes a feedback request strategy for indicating the unreliable bits, is presented and its performance is investigated. The simulation results show that the network throughput can be significantly improved by the proposed scheme, compared to traditional CDMA-based automatic repeat request (ARQ). Moreover, under the context of cognitive radio networks, we propose a hybrid strategy in which interleave division multiplexing (IDM) is used during whole-packet retransmission, and demonstrate the effectiveness of the proposed scheme with and without the hybrid strategy as well as give insights about the throughput performance under different parameter settings.