The COVID-19 pandemic continues spreading rapidly around the world and has caused devastating outcomes towards the health of the global population. The reverse transcription-polymerase chain reaction (RT-PCR) test, as the only current gold standard for screening infected cases, yields a relatively high false positive rate and low sensitivity on asymptomatic subjects. The use of chest X-ray radiography (CXR) images coupled with deep- learning (DL) methods for image classification, represents an attractive adjunct to or replacement for RT-PCR testing. However, its usage has been widely debated over the past few months and its potential effectiveness remains unclear. A number of DL-based methods have been proposed to classify the COVID-19 cases from the normal ones, achieving satisfying high performance. However, these methods show limited performance on the multi-class classification task for COVID-19, pneumonia and normal cases, mainly due to two factors: 1) the textures in COVID-19 CXR images are extremely similar to that of pneumonia cases, and 2) there are much fewer COVID-19 cases compared to the other two classes in the public domain. To address these challenges, a novel framework is proposed to learn a deep convolutional neural network (DCNN) model for accurately classifying COVID-19 and pneumonia cases from other normal cases by the use of CXR images. In addition to training the model by use of conventional classification loss which measures classification accuracy, the proposed method innovatively employs a reconstruction loss measuring image fidelity and an adversarial loss measuring class distribution fidelity to assist in the training of the main DCNN model to extract more informative features to support multi-class classification. The experiment results on a COVID-19 dataset demonstrate the superior classification performance of the proposed method in terms of accuracy compared to other existing DL-based methods. The experiment on another cancer dataset further implies the potential of applying the proposed methods in other medical imaging applications.