This study focuses on the inverse nodal problem for a singular diffusion equation that involves eigenparameter-dependent terms and internal discontinuities. First, we derive reconstruction formulas for the potential function q(x) and the parameter β using nodal data, applying the Chebyshev interpolation method in the limiting process. Next, we establish the stability of the inverse problem through rigorous analysis. Finally, approximate solutions are obtained using a numerical approach based on Chebyshev polynomials. To evaluate the effectiveness of the method, numerical experiments are conducted with MATLAB, comparing the results to those obtained through classical solution techniques.