The aim of this paper is to investigate the recently developed mixed-ADC architecture for frequency-selective channels. Multi-carrier techniques such as orthogonal frequency division multiplexing (OFDM) are employed to handle inter-symbol interference (ISI). A frequency-domain equalizer is designed for mitigating the inter-carrier interference (ICI) introduced by the strong nonlinearity of coarse quantization. For static single-input-multiple-output (SIMO) channels, a closed-form expression of the generalized mutual information (GMI) is derived, and based on which the linear frequency-domain equalizer is optimized. The analysis is then extended to ergodic time-varying SIMO channels, where numerically tight lower and upper bounds of the GMI are derived. The analytical results are naturally applicable to the multi-user scenario, for both static and time-varying fading channels. Extensive numerical studies reveal that the mixed-ADC architecture with a small proportion of high-resolution ADCs is sufficient to achieve a large portion of the capacity of ideal conventional architecture, and that it is effective in eliminating the error floor encountered by receivers with coarse quantization only.