A physics-informed neural network (PINN) algorithm is applied to precisely measure the thickness of multiple layers of automotive paint with terahertz time-domain spectroscopy (THz-TDS). This technique overcomes the inherent uncertainty of traditional THz-TDS measurements with model inversion algorithms due to the multiple paint layers with uncertain boundaries. The simplest multilayer perception (MLP) based model for the paint is used with a hybrid convolution neural network with long short-term memory (CNN-LSTM) deep learning model approach. Measurement accuracy is better than 3.3 µm for three-layer paint and 4.3 µm for five layers with discrimination of thickness difference of less than 1 µm for five-payer paint thicknesses ranging from 4.5 to 55 µm.