Localized surface plasmon resonance (LSPR) of metallic nanoparticles (NPs) can generate and enhance the nonlinear optical (NLO) response and has been widely used in biosensing, optical bistability, optical switch, and modulator, surface-enhanced spectroscopies, etc. Here, the two-dimensional (2D) Au & Ag hybrid plasmonic NP network (Au & Ag HPNN) were synthesized by assembling Au and Ag NPs in ethanol solvent and transferring onto a CaF2 substrate. The frequency-domain finite element method (FEM) simulations were performed to explore their LSPR properties, demonstrating the broadband optical responses throughout visible, near-infrared and mid-infrared regions. The ultrafast carrier relaxation times were determined to be 3.9, 5.6, and 8.6 ps, while the nonlinear absorption coefficients were −1.12 × 104, −1.71 × 104, and −2.54 × 104 cm/GW, respectively, for the three wavelengths matching the LSPRs peaks at 1.0, 2.0, and 3.0 μm bands. Furthermore, passively Q-switched (PQS) solid-state lasers operating at 1062.8, 1990.8, and 2947 nm were demonstrated with 2D Au & Ag HPNN based saturable absorbers. This work not only reveals desirable ultrafast broadband NLO responses of 2D HPNN, but also provides a platform for investigating their applications in nanophotonic devices.