Home energy management systems (HEMSs) enable residential customers to efficiently participate in demand response programs in order to obtain optimal benefits. Traditional HEMSs only manage household electric appliances to reduce the electricity consumption cost while the optimal scheduling of natural gas appliances has been overlooked. Due to the increasing popularity of natural gas appliances in modern smart homes, the electricity consumption of residential customers connected to the natural gas network is significantly affected by the use of natural gas appliances. To consider the interaction between electric and natural gas appliances in households, a day-ahead optimal joint scheduling model of electric and natural gas appliances for HEMS is proposed. Firstly, all household appliances are classified into several categories and the mathematical model of each appliance is presented. Then, a day-ahead optimal joint scheduling model of both electric and natural gas appliances for HEMS is formulated, in which the objective function is to minimize the household's energy cost and the dissatisfaction level caused by the shifting, reduction and replacement of loads in response to the time varying prices. Case studies using realistic data indicate that the proposed model can save the total energy costs up to 30% for customers whilst ensuring their satisfaction levels. INDEX TERMS Home energy management system, natural gas, demand response, joint scheduling, dissatisfaction. A. SUPERSCRIPTS bch Battery charging bdch Battery discharging dw Dishwasher eac Electric air conditioner el Electric light es Electric stove ev Electric vehicle ewh Electric water heater gahs Gas air heating system The associate editor coordinating the review of this manuscript and approving it for publication was Alexander Micallef. gs Gas stove gwh Gas water heater ua Uncontrollable appliance s Stove wh Water heater wm Washing machine B. INDEXES AND SETS