This paper presents a new structural health monitoring strategy based on a deep learning architecture that uses nonlinear ultrasonic signals for the automatic assessment of breathing-like debonds in lightweight stiffened composite panels (SCPs). Towards this, nonlinear finite element simulations of ultrasonic guided wave (GW) response of SCPs and laboratory-based experiments have been undertaken on multiple composite panels with and without baseplate-stiffener debonds using fixed a network of piezoelectric transducers (actuators/sensors). GW signals in the time domain are collected from the network of sensors onboard the SCPs and these signals in the frequency domain represent nonlinear signatures as the existence of higher harmonics. These higher harmonic signals are separated from the GWs (raw) and converted to images of time–frequency scalograms using continuous wavelet transforms. A deep learning architecture is designed that uses the convolutional neural network to automatically extract the discrete image features for the characterization of SCP under healthy and variable breathing-debond conditions. The proposed deep learning-aided health monitoring strategy demonstrates a promising autonomous inspection potential with high accuracy for such complex structures subjected to multi-level breathing-debond regions.