Laser nanostructuring of thin films with ultrashort laser pulses is widely used for nanofabrication across various fields. A crucial parameter for optimizing and understanding the processes underlying laser processing is the absorbed laser fluence, which is essential for all damage phenomena such as melting, ablation, spallation, and delamination. While threshold fluences have been extensively studied for single compound thin films, advancements in ultrafast acoustics, magnetoacoustics, and acousto-magneto-plasmonics necessitate understanding the laser nanofabrication processes for functional multilayer films. In this work, we investigated the thickness dependence of ablation and delamination thresholds in Ni/Au bilayers by varying the thickness of the Ni layer. The results were compared with experimental data on Ni thin films. Additionally, we performed femtosecond time-resolved pump-probe measurements of transient reflectivity in Ni to determine the heat penetration depth and evaluate the melting threshold. Delamination thresholds for Ni films were found to exceed the surface melting threshold suggesting the thermal mechanism in a liquid phase. Damage thresholds for Ni/Au bilayers were found to be significantly lower than those for Ni and fingerprint the non-thermal mechanism without Ni melting, which we attribute to the much weaker mechanical adhesion at the Au/glass interface. This finding suggests the potential of femtosecond laser delamination for nondestructive, energy-efficient nanostructuring, enabling the creation of high-quality acoustic resonators and other functional nanostructures for applications in nanosciences.