Ambient backscatter communication is an energy efficient technique for massive Internet of Things (IoT). Combining with flexibly deployed unmanned aerial vehicles (UAVs), the UAV-aided ambient backscatter communication can establish wireless links for isolated IoT nodes efficiently. In this paper, we investigate the outage performance of the UAV-aided air-ground network with underlaid ambient backscatter communications, where the emitted signals from the air-ground link are leveraged as radio frequency (RF) carrier for ambient backscattering. The air-ground channel is modeled as a probabilistic line-of-sight (LoS) channel with Nakagami- $m$ fading. Then, the ground communication is modeled as a non-line-of-sight (NLoS) channel with Rayleigh fading. For the downlink, we derive the expressions of the outage probabilities of the backscatter link and the air-ground link. In addition, the asymptotic cases of infinite transmit power and infinite fading parameter are analyzed. For the uplink, the outage probabilities of the backscatter link and air-ground are analyzed, with the cases of infinite transmit power and fading parameter discussed. Simulation results show that the analytical results match well with the Monte Carlo results, which verifies the effectiveness of the proposed scheme.