Two-dimensional (2D) Janus monolayers represent a novel class of materials characterized by their unique structures and exceptional properties. The excitonic characteristics, along with the linear and nonlinear optical responses of the 2D MA2Z4 family, have been systematically investigated through first-principles calculations. The findings indicate that monolayers of MSiGeN4 (M = Mo or W) exhibit a pronounced second harmonic generation (SHG) response and notable infrared transmission capabilities, due to the breaking of mirror symmetry in these materials. A comparative analysis of the SHG response of intrinsic MSi2N4 (M = Mo and W) monolayers demonstrates that Janus MSiGeN4 (M = Mo and W) monolayers significantly enhance the SHG response, with enhancement factors of 5.5 and 3.8 at infrared wavelengths (1064 nm). The Janus monolayers also exhibit an additional out-of-plane response, thus enhancing the efficiency of incident light utilization from all directions. Specifically, the out-of-plane response of Janus WSiGeN4 monolayers is 1.1 pm/V greater than the in-plane response of intrinsic WSi2N4. Furthermore, the dependence of SHG polarizability indicates that the out-of-plane polarizability significantly modifies the SHG response as a function of the incident angle θ. As a derivative of the 2D MA2Z4 family, MSiGeN4 (M = Mo and W) expands the scope of 2D Janus materials, and these findings may inform the design and synthesis of innovative 2D nonlinear optical materials.