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A key issue in federated learning over wireless channels is how to exchange a large number of the model parameters via time-varying channels. Two types of solutions based on digital and analog schemes are used typically. The digital-based solution takes quantization and entropy coding for compression, whereas transmissions via wireless channels may cause catastrophic errors owing to the all-or-nothing behavior in entropy coding. The analog-based solutions such as AirNet and AirComp use analog modulation for the parameter transmissions. However, such an analog scheme often causes significant distortion due to the source signal's large power without compression gain. This paper proposes a novel hybrid digital-analog transmission-Federated AirNet--for the model parameter transmissions in federated learning. The Federated AirNet integrates low-rate digital coding and energy-compact analog modulation. The digital coding offers the baseline of the model parameters and compacts the source signal power. In addition, the residual parameters, which are obtained from the original and encoded model parameters, are analog-modulated to enhance the baseline according to the instantaneous wireless channel quality. We show that the proposed Federated AirNet yields better image classification accuracy compared with the digital-based and analog-based solutions over a wide range of wireless channel signal-to-noise ratios (SNRs).