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The finite-difference time-domain (FDTD) method is a widely used numerical technique for simulating electromagnetic wave interactions with complex media. Various efficient approaches have been used to analyze complex media, and the surface impedance boundary condition (SIBC) is one of the most powerful techniques in FDTD simulations, allowing efficient electromagnetic modeling of lossy materials. However, conventional SIBC-FDTD formulations face challenges when analyzing lossy dispersive materials because of the assumption of frequency-independent relative permittivity and conductivity in the inverse Laplace transform. To address this, we propose a dispersion-modeling approach for the surface impedance of lossy dispersive materials. Additionally, to reduce grid errors in the FDTD discrete domain, we introduce the surface admittance boundary condition (SABC) for lossy dispersive materials. We investigated the numerical accuracy by deriving the numerical surface impedance and admittance for the proposed surface boundary condition (SBC)-FDTD formulations. In addition, we determined the numerical stability conditions of the SBC-FDTD formulations using the von Neumann method combined with the Routh-Hurwitz criterion. Numerical examples validate both the numerical accuracy and stability of the proposed SBC-FDTD formulations. Our findings enhance the understanding and application of the SBC in FDTD simulations, especially for lossy dispersive materials, and provide insights for future research and electromagnetic modeling in various fields. [ABSTRACT FROM AUTHOR]