The combination of single-pixel-imaging and single-photon-counting technology can achieve ultrahigh-sensitivity photon-counting imaging. However, its applications in high-resolution and real-time scenarios are limited by the long sampling and reconstruction time. Deep-learning-based compressive sensing provides an effective solution due to its ability to achieve fast and high-quality reconstruction. This paper proposes a sampling and reconstruction integrated neural network for single-photon-counting compressive imaging. To effectively remove the blocking artefact, a subpixel convolutional layer is jointly trained with a deep reconstruction network to imitate compressed sampling. By modifying the forward and backward propagation of the network, the first layer is trained into a binary matrix, which can be applied to the imaging system. An improved deep-reconstruction network based on the traditional Inception network is proposed, and the experimental results show that its reconstruction quality is better than existing deep-learning-based compressive sensing reconstruction algorithms.