The novel Coronavirus disease (COVID-19), which first appeared at the end of December 2019, continues to spread rapidly in most countries of the world. Respiratory infections occur primarily in the majority of patients treated with COVID-19. In light of the growing number of COVID-19 cases, the need for diagnostic tools to identify COVID-19 infection at early stages is of vital importance. For decades, chest X-ray (CXR) technologies have proven their ability to accurately detect respiratory diseases. More recently, with the availability of COVID-19 CXR scans, deep learning algorithms have played a critical role in the healthcare arena by allowing radiologists to recognize COVID-19 patients from their CXR images. However, the majority of screening methods for COVID-19 reported in recent studies are based on 2D convolutional neural networks (CNNs). Although 3D CNNs are capable of capturing contextual information compared to their 2D counterparts, their use is limited due to their increased computational cost (i.e. requires much extra memory and much more computing power). In this study, a transfer learning-based hybrid 2D/3D CNN architecture for COVID-19 screening using CXRs has been developed. The proposed architecture consists of the incorporation of a pre-trained deep model (VGG16) 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 to be predicted: 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.