High peak and average power lasers with high wall-plug efficiency, like the Big Aperture Thulium (BAT) laser, have garnered tremendous attention in laser technology. To meet the requirements of the BAT laser, we have developed low-dispersion reflection multilayer dielectric (MLD) gratings suitable for compression of high-energy pulses for operations at 2 micron wavelength. We carried out 10000-on-1 damage tests to investigate the fluence damage thresholds of the designed MLD gratings and mirrors, which were found between 100-230 mJ/cm2. An ultrashort pulsed laser (FWHM = 53 fs, λ = 1.9 μm) operating at 500 Hz was used in the serpentine raster scans. The atomic force microscope images of the damage sites show blister formation of the underlying layers at lower fluences but ablation of the grating pillars at higher fluences. We simulated the dynamic electronic excitation in the MLD optics with a finite-difference in the time domain approach in 2D. The simulation results agree well with the LIDT measurements and the observed blister formation. This model is able to evaluate the absolute LIDT of MLD gratings.