With the growing interdependence between the electricity system and the natural gas system, the operation uncertainties in either subsystem, such as wind fluctuations or component failures, could have a magnified impact on the reliability of the whole system due to energy interactions. A joint reserve scheduling model considering the cross-sectorial impacts of operation uncertainties is essential but still insufficient to guarantee the reliable operation of the integrated electricity and natural gas system (IEGS). Therefore, this paper proposes a day-ahead security-constrained unit commitment (SCUC) model for the IEGS to schedule the operation and reserve simultaneously considering reliability requirements. Firstly, the multi-state models for generating units and gas wells are established. Based on the multi-state models, the expected unserved energy cost (EUEC) and the expected wind curtailment cost (EWC) criteria are proposed based on probabilistic methods considering wind fluctuation and random failures of components in IEGS. Furthermore, the EUEC and EWC criteria are incorporated into the day-ahead SCUC model, which is nonconvex and mathematically reformulated into a solvable mixed-integer second-order cone programming (MISOCP) problem. The proposed model is validated using an IEEE 30-bus system and Belgium 20-node natural gas system. Numerical results demonstrate that the proposed model can effectively schedule the energy reserve to guarantee the reliable operation of the IEGS considering the multiple uncertainties in different subsystems and the cross-sectorial failure propagation.