Triple-layered structures, containing gold nanoparticles (AuNP), namely AuNP(6 nm)–Al₂O₃(1.5 nm)–PdO(17 nm), sample #1, and AuNP(6 nm)–Al₂O₃(13 nm)–PdO(17 nm), sample #2, were obtained on glass substrates. A significant difference in the structure of their absorption spectra in the vicinity of the plasmon resonance of gold nanoparticles indicates a dependence on the mutual influence of the AuNP and PdO layers on the thickness of the Al₂O₃ insulating layer. Optical cubic nonlinearity (OCN) parameters, namely n₂, Reχ⁽³⁾, and Imχ⁽³⁾, were determined for nanosecond pulsed laser excitation at λ = 1064 nm (τ_p = 15 ns) and λ = 532 nm (τ_p = 9 ns). It is shown that under 1064 nm excitation: (i) the sign of the refractive nonlinearity of the structures depends on the way they are illuminated in a Z-scan experiment, being positive when the laser beam impinges from the AuNP side (geometry A) and negative if the beam falls from the PdO side (geometry B); (ii) the nonlinear index of refraction n₂ = 2.5 × 10^–7 cm²/W of the structure #1 with a 1.5 nm thick Al₂O₃ layer is significantly larger than n₂ = 0.9 × 10^–7 cm²/W of the structure #2 with a 13 nm Al₂O₃ layer; (iii) the refractive nonlinearity of triple-layer structures is larger than that of double-layer structures AuNP-Al₂O₃; (iv) both double and triple-layer structures demonstrate moderate non linear absorption (β ~ 10^–2 cm/W), probably due to two-photon transitions between the d and sp bands of AuNP. For 532 nm excitation, the refractive nonlinearity of the triple layer structures is negative with |n₂|~ 10^–6 cm²/W irrespective of the geometry of the Z-scan experiment. For both samples #1 and #2 with different thickness of Al₂O₃ the value of |n₂| is sufficiently larger than one for separate PdO film. This may be explained by the strong influence of interaction of processes in the AuNP and conductive PdO layers. The nonlinear absorption coefficient β is negative (saturable absorption) in AuNP-Al₂O₃ structures and positive in AuNP-Al₂O₃-PdO structures.