Monitoring COVID-19 patients with COPD has become one of the major tasks in preventing transmission and delivering emergency healthcare services after vaccination in case of any issues. Most COVID-19-affected patients are suggested to self-quarantine at home or in institutionalized quarantine centers. In such cases, it is essential to provide remote healthcare services. For remote healthcare monitoring, two approaches are being considered in this study, which include mHealth and Telehealth. A mixed-methods approach is adopted, where survey questionnaires are used for collecting information from 108 patients and semi-structured interviews are used with seven physicians regarding mHealth and Telehealth approaches. Survey results indicated that mHealth is rated to be slightly more effective than Telehealth, and interview results indicated that Telehealth is identified to be slightly more effective than mHealth in relation to parameters including usefulness, ease of use and learnability, interface and interaction quality, reliability, and satisfaction. However, both physicians and patients opined that both mHealth and Telehealth have a promising future with increasing adoption. Based on the findings, it can be concluded that both mHealth and Telehealth are considered to be effective in delivering remote care for COPD patients infected with COVID-19 at home. Implications of the study findings are discussed.