The SiNx/Si/SiNx multi-layer film is prepared by radio-frequency magnetron sputtering and thermal annealing. The average grain size of nanocrystalline silicon, the optical band-gap and the nonlinear absorption coefficient at 1064 nm laser are characterized and estimated. The rate-equation theoretical model of the dual-wavelength laser passively Q-switched by SiNx/Si/SiNx multi-layer film is established and the dynamics of the dual-wavelength pulse formation is numerically calculated. Simultaneous dual-wavelength passive Q-switching is realized in a laser diode (LD) end-pumped three-mirror compound resonator Nd:YVO4 laser using SiNx/Si/SiNx film as the saturable absorber. Both 1064 nm pulse with 20 ns duration and 1342 nm pulse with 19 ns duration are obtained. The results show that dual-wavelength passive Q-switching mainly results from two-photon saturable absorptions for 1064 nm and 1342 nm lasers, and that the difference of output losses between the two overlapping collinear cavities and the relative nonlinear absorption coefficients for dual-wavelength lasers influence the pulse durations and time separation of dual-wavelength pulses.