This paper presents an efficient integration of a flash-binary geothermal system with a double-pressure Kalina cycle and a proton exchange membrane electrolyzer unit. The main objective is to generate power and hydrogen simultaneously. A comprehensive thermodynamic analysis is conducted, encompassing mass, energy, and exergy assessments, along with an exergo-economic approach, to thoroughly evaluate system performance. The operation of the system is examined under varying conditions, and trends in the assessment indexes are predicted accordingly. The designed system achieves notable results, producing 1018 kW of net power and 0.1119 kg/h of hydrogen. The thermal and exergetic efficiencies are found to be 14.34 % and 45.59 %, respectively, based on the thermodynamic approach. From an economic perspective, the payback period is estimated to be 2.51 years, while the sum unit cost of products is calculated at 8.94 $/GJ. Furthermore, a detailed exergy analysis highlights that the Kalina cycle's condenser contributes the most to exergy destruction, accounting for approximately 129.6 kW. Through a parametric study, it is revealed that the pressure of the production well significantly influences the performance indicators, and the price of electricity sold has a substantial impact on the system's payback period and net present value. Moreover, the application of a multi-objective optimization strategy leads to the identification of the system's optimal state through an exergo-economic assessment. This optimization yields an exergy efficiency of around 49.75 % and a sum unit cost of products of 8.56 $/GJ.