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Liquefying hydrogen is an efficient way to store and transport hydrogen. However, the hydrogen liquefaction process is energy intensive. Therefore, an integrated liquefaction process of hydrogen and natural gas utilizing the mixed refrigerant cycle and the hydrogen Claude cycle is proposed. The process not only couples a steam methane reforming process to produce hydrogen and a carbon dioxide refrigeration cycle to assist in pre-cooling, but also employs a solar energy absorption refrigeration system to enhance energy efficiency. The proposed process is simulated and optimized using HYSYS and the particle swarm optimization algorithm, and energy, exergy, and economic analyses are performed. The energy analysis shows that the specific energy consumption of the proposed process is 5.2201 kWh/kg, a reduction of 10.67% compared to the base case. The exergy loss and exergy efficiency are 64,904 kW and 62.21%, which are 13.63% and 6.63% lower than the base case, respectively. The economic analysis shows that the total annualized cost of the process is USD 28.6 million per year. The proposed integrated liquefaction process not only realizes the high efficiency of energy utilization but also follows the development trend of integrated energy systems.