So far, COVID-19, the novel coronavirus, continues to spread rapidly in most countries of the world, putting people's lives at risk. According to the WHO, respiratory infections occur primarily in the majority of patients treated with COVID-19. For decades, chest X-ray (CXR) technologies have proven their ability to accurately detect and treat respiratory diseases. Deep learning techniques, as well as the availability of a large number of CXR samples, have made a significant contribution to the fight against this pandemic. However, the most common screening methods are based on 2D CNNs, since 3D counterparts are enormously costly and labor-intensive. In this study, a hybrid 2D/3D convolutional neural network (CNN) architecture for COVID-19 screening using CXRs has been developed. The proposed architecture consists of the incorporation of a pre-trained deep model (VGG-16) and a shallow 3D CNN, combined with a depth-wise separable convolution layer and a spatial pyramid pooling module (SPP). Specifically, the depth-wise separable convolution helps to preserve the useful features while reducing the computational burden of the model. The SPP module is designed to extract multi-level representations from intermediate ones. Experimental results show that the proposed framework can achieve reasonable performances when evaluated on a collected dataset (3 classes: COVID-19, Pneumonia, and Normal). Notably, it achieved a sensitivity of 98.33%, a specificity of 98.68% and an overall accuracy of 96.91%