We propose a modified x-ray form factor that describes the scattering cross section in warm dense matter valid for both the plasma and the solid (crystalline) state. Our model accounts for the effect of lattice correlations on the electron-electron dynamic structure, as well as provides a smooth transition between the solid and the plasma scattering cross sections. In addition, we generalize the expression of the dynamic structure in the case of a two-temperature system (with different electron and ion temperatures). This work provides a unified description of the x-ray scattering processes in warm and dense matter, as the one encountered in inertial confinement fusion, laboratory astrophysics, material science, and high-energy density physics and it can be used to verify temperature relaxation mechanisms in such environments.