We developed a ballistocardiography (BCG)-based Internet-of-Medical-Things (IoMT) system for remote monitoring of cardiopulmonary health. The system composes of BCG sensor, edge node, and cloud platform. To improve computational efficiency and system stability, the system adopted collaborative computing between edge nodes and cloud platforms. Edge nodes undertake signal processing tasks, namely approximate entropy for signal quality assessment, a lifting wavelet scheme for separating the BCG and respiration signal, and the lightweight BCG and respiration signal peaks detection. Heart rate variability (HRV), respiratory rate variability (RRV) analysis and other intelligent computing are performed on cloud platform. In experiments with 25 participants, the proposed method achieved a mean absolute error (MAE)±standard deviation of absolute error (SDAE) of 9.6±8.2 ms for heartbeat intervals detection, and a MAE±SDAE of 22.4±31.1 ms for respiration intervals detection. To study the recovery of cardiopulmonary function in patients with coronavirus disease 2019 (COVID-19), this study recruited 186 discharged patients with COVID-19 and 186 control volunteers. The results indicate that the recovery performance of the respiratory rhythm is better than the heart rhythm among discharged patients with COVID-19. This reminds the patients to be aware of the risk of cardiovascular disease after recovering from COVID-19. Therefore, our remote monitoring system has the ability to play a major role in the follow up and management of discharged patients with COVID-19.