Quantization is of significance for compressing the over-parameterized deep neural models and deploying them on resource-limited devices. Fixed-precision quantization suffers from performance drop due to the limited numerical representation ability. Conversely, mixed-precision quantization (MPQ) is advocated to compress the model effectively by allocating heterogeneous bit-width for layers. MPQ is typically organized into a searching-retraining two-stage process. Previous works only focus on determining the optimal bit-width configuration in the first stage efficiently, while ignoring the considerable time costs in the second stage. However, retraining always consumes hundreds of GPU-hours on the cutting-edge GPUs, thus hindering deployment efficiency significantly. In this paper, we devise a one-shot training-searching paradigm for mixed-precision model compression. Specifically, in the first stage, all potential bit-width configurations are coupled and thus optimized simultaneously within a set of shared weights. However, our observations reveal a previously unseen and severe bit-width interference phenomenon among highly coupled weights during optimization, leading to considerable performance degradation under a high compression ratio. To tackle this problem, we first design a bit-width scheduler to dynamically freeze the most turbulent bit-width of layers during training, to ensure the rest bit-widths converged properly. Then, taking inspiration from information theory, we present an information distortion mitigation technique to align the behaviour of the bad-performing bit-widths to the well-performing ones. In the second stage, an inference-only greedy search scheme is devised to evaluate the goodness of configurations without introducing any additional training costs. Extensive experiments on three representative models and three datasets demonstrate the effectiveness of the proposed method.