This paper presents a novel optimal offering framework to incorporate hydrogen system potential for frequency regulation goals. Furthermore, the presented model considers the possibility of submitting bids for a day-ahead hydrogen market. To harness the uncertainty of AGC (automatic generation control) signals, the problem is formulated as a two-level stochastic programming approach where in the first stage, the day-ahead market is cleared, and in the second stage, which is related to the real-time market, the up and down capacities of the hydrogen system are determined for each hour. The results indicate that the presented model is able to maximize the income of the integrated power/hydrogen system by determining the optimal scheduling of each of these devices and increase the income of the system by taking advantage of the frequency regulation market and dedicating a capacity of the electrolyzer and fuel cell to this market.