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Unit maintenance and unit commitment are two critical and interrelated aspects of electric power system operation, both of which face the challenge of coordinating efforts to enhance reliability and economic performance. This challenge becomes increasingly pronounced in the context of increased integration of renewable energy and flexible loads, such as wind power and electric vehicles, into the power system, where high uncertainty is prevalent. To tackle this issue, this paper develops a two-stage adaptive robust optimization model for the joint unit maintenance and unit commitment strategy. The first stage focuses on making joint decisions regarding unit maintenance and unit commitment, while the second stage addresses economic dispatch under the worst-case scenarios of wind power and load demand. Then a practical solution methodology is proposed to solve this model efficiently, which combines the inexact column-and-constraint generation algorithm with an outer approximation method. Finally, the economic viability and adaptability of the proposed method is demonstrated based on the RTS-79 test system.