In this paper, a bit-interleaved coded modulation (BICM)scheme with an iterative receiver is proposed for asynchronous cooperative communications. In such environments, synchronous errors may be severe because relays experience different environments. Rather than treating synchronous errors as impairments, this study focuses on exploiting possible benefits of them, particularly of the possible multiple carrier frequency offsets (MCFOs). With the proposed scheme, potential space diversity of multiple relays with MCFOs is manifested as time diversity, which in turn is harvested through the carefully-designed iterative receiver. The system achieves improved diversity gain and is extremely robust even when all asynchronous parameters, including multiple Doppler effects, are considered.