H₂ molecule and their isotopes represent one of the modern clean energy sources. It is imperative to understand their thermodynamic properties for comprehending their behaviors under various conditions. Thereby promoting their more in-depth applications. In this paper, an extended improved multiparameter exponential-type potential (EIMPET) combined with the quantum statistical ensemble theory is used to investigate and analyze the thermodynamic properties of H₂ and HD molecules. Firstly, reliable energy level data for molecules are obtained using the EIMPET potential. Subsequently, the one-dimensional Schrödinger equation is solved with the LEVEL program to determine the rovibrational energy levels of the molecules. Finally, the quantum statistical ensemble theory is integrated to determine the partition functions, molar heat capacity, molar entropy, molar enthalpy, and reduced molar Gibbs free energy of H₂ and HD in a temperature range of 100–6000 K. The calculation results indicate that compared with IHH potential and IMPET potential, the EIMPET potential is closer to RKR data. A comparison of the calculated thermodynamic properties of the molecules reveals that the results from the EIMPET potential-based method accord well with those from the NIST database. Specifically, for H₂, the root mean square (RMS) errors for C_\textm\left( T \right) , S_\textm\left( T \right) , G_\textr\left( T \right) , and \Delta H_\textr\left( T \right) are 0.6894 J·K^–1·mol^–1, 0.3824 J·K^–1·mol^–1, 0.1754 J·K^–1·mol^–1, and 0.9586 kJ·mol^–1, respectively, while for HD, the RMS errors are 0.3431 J·K^–1·mol^–1, 0.1443 J·K^–1·mol^–1, 0.0495 J·K^–1·mol^–1, and 0.4863 kJ·mol^–1, respectively. All of these results are superior to those obtained using IMPET potential, and to those obtained using IHH potential as a whole. These findings demonstrate the advantages and practical applications of the EIMPET potential in calculating the thermodynamic properties of diatomic gas molecules, providing a foundation for subsequently studying the thermodynamic properties of triatomic molecules.