We investigate two-photon transitions to the electron-hole scattering continuum in monolayer transition-metal dichalcogenides, and identify two contributions to this nonlinear optical process with opposite circularly polarized valley selection rules. In the non-interacting limit, the competition between the two contributions leads to a crossover of the selection rule with the increase of the two-photon energy. With the strong Coulomb interaction between the electron and hole, the two contributions excite electron-hole scattering states in orthogonal angular momentum channels, while the strength of the transition can be substantially enhanced by the interaction. Based on this picture of the two-photon transition, the second harmonic generation (SHG) in the electron-hole continuum is analyzed, where the Coulomb interaction is shown to greatly alter the relative strength of different cross-circular polarized SHG processes. Valley current injection by the quantum interference of one-photon and two-photon transition is also investigated in the presence of the strong Coulomb interaction, which significantly enhances the injection rate.
