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The increasing number of gas-fired units has significantly intensified the coupling between power and gas networks. Traditionally, the nonlinearity and nonconvexity in gas flow equations, together with renewable-induced stochasticity, result in a computationally expensive model for unit commitment in electricity-gas coupled integrated energy systems (IES). To accelerate stochastic day-ahead scheduling, we applied and modified Progressive Hedging (PH), a heuristic approach that can be computed in parallel to yield scenario-independent unit commitment. By applying a termination and enumeration technique, the modified PH algorithm saves considerable computational time, especially when the unit production prices are similar for all generators, and when the scale of IES is large. Moreover, an adapted second-order cone relaxation (SOCR) is utilized to tackle the nonconvex gas flow equation. Case studies are performed on the IEEE 24-bus system/Belgium 20-node gas system and the IEEE 118-bus system/Belgium 20-node gas system. The computational efficiency when employing PH is 188 times that of commercial software, even outperforming Benders Decomposition. Meanwhile, the gap between the PH algorithm and the benchmark is less than 0.01% in both IES systems, which proves that the solution produced by PH reaches acceptable optimality in this stochastic UC problem.