Pulsed eddy current (PEC) testing is a nondestructive testing (NDT) method, which is highly suitable for thickness measurement and sub-surface-defect detection. In this article, PEC testing is employed to simultaneously detect defect and sample thickness. First, a finite-element method (FEM) is conducted to reveal the signal characteristics of different defect sizes and depths on the aluminum plate, as well as its thickness. Experimental verification is conducted to verify the simulation results. It reveals that the signal variations associated with defect size and depth are relatively smaller compared to the impact of thickness changes. Both logarithmic function and discrete Fourier transform (DFT) are utilized as a signal processing method to improve signal differentiation between defect characteristics. Notably, the processed signal through DFT produces both amplitude and phase spectra, with a focus on the enriched features within the high-frequency portion of the signals post-DFT. Finally, all the raw and processed data are fed into deep learning (DL) models. The optimized Res2net18 network with post-DFT data demonstrates superior performance. It achieves classification accuracies of 98.0%, 100%, and 96.0% for defect size, thickness of the sample, and defect depth, respectively. The results show that the proposed DL network has faster convergence and stability in comparison to the Res2Net network and DenseNet121, and there are 1.5% and 2.0%, and 5.4% and 9.7% classification accuracy improvement in defect size and depth. The predicted values based on the optimized Res2Net network also present consistent results with validation and test results.