This paper presents an integrative demand response (DR) mechanism for energy management of appliances, an energy storage system and an electric vehicle (EV) within a home. The paper considers vehicle-to-home (V2H) and vehicle-to-grid (V2G) functions for energy management of EVs and the degradation cost of the EV battery caused by the V2H/V2G operation in developing the proposed DR mechanism. An efficient optimization algorithm is developed based on approximate dynamic programming, which overcomes the challenges of solving high dimensional optimization problems for the integrative home energy system. To investigate how the participation of different home appliances affects the DR efficiency, several DR scenarios are designed. Then, a detailed simulation study is conducted to investigate and compare home energy management efficiency under different scenarios.