We analyze the performance of an orthogonal frequency-division multiplexing interleave-division multiple access (OFDM-IDMA) system for channels with a carrier frequency offset. First we introduce a vector-valued transmission model for the OFDM-IDMA system, including an improved chip detector. A semi-analytical technique is applied to generate variance transfer charts and predict the performance of the iterative receiver. Based on this analysis and Monte Carlo simulations we conclude that the performance of OFDM-IDMA over channels with carrier frequency offset is improved substantially by the new receiver concept.