This paper presents a stochastic security-constrained unit commitment (SCUC) model for the optimal midterm and flexible allocations of hydro and natural gas systems when accommodating a large integration of wind energy. Random errors in forecasting the hourly wind, natural water inflow, and electric load as well as random outages of power system components are modeled in scenarios via the Monte Carlo (MC) simulation. The proposed optimization model is formulated as a two-stage stochastic problem, where short-term and midterm generation resource optimizations are investigated in the first and the second stages, respectively. The reliability criteria including the loss of load expectation (LOLE) and load curtailment limits are incorporated into the midterm stochastic SCUC problem, where electric power and natural gas network constraints are checked. Numerical experiments signify the effectiveness of the proposed method for the midterm optimal scheduling of water and natural gas flexibilities when integrating wind energy resources.