Developing integrated energy systems has been considered a feasible pathway to renewable-powered energy systems. The power to hydrogen technology is recognized as a promising method to enhance the economics of integrated energy systems and help reduce renewable curtailments. However, oxygen-enriched gas, which is the by-product of power to hydrogen processes (electrolysation), has not been fully utilized yet. It can be purified to produce medical oxygen at a low cost and may further increase the economics of integrated energy systems. Particularly, at this very moment, the consideration of the combined production of hydrogen and medical oxygen also has the potential in relieving the shortage of medical oxygen due to the outbreak of the 2019 novel coronavirus (COVID-19). This paper proposes a model for the operation of integrated energy systems which considers the combined production of hydrogen and medical oxygen. This model is formulated as a convex mixed-integer optimization problem which balances the electricity，heat and hydrogen demands every hour in a 24-hour period and balances oxygen demand on a daily basis. In order to find the global optimal solution, this paper uses Yalmip calling Gurobi to seek the most economic unit dispatch strategy. A test case of Taizhou City has been studied and showed that the combined production of hydrogen and medical oxygen improves the integrated energy system economics.