The tetragonal rare-earth transition-metal silicide system with three-dimensional crystallographic structure , where is Dy, Ho, Er, Tm, and Lu, and and Rh, has been shown to exhibit fascinating charge-density-wave (CDW) phase transitions, a phenomenon largely found in otherwise low-dimensional systems. In this study, we report the investigations of CDW in DyIrSi at different temperatures using transmission electron microscopy techniques including electron diffraction and dark-field imaging. Incommensurate superlattice spots along the axis were observed in the electron-diffraction patterns when the sample was cooled below the CDW transition temperature at 208 K. CDW becomes commensurate with further cooling and configurations of CDW dislocations convincingly show that the CDW phase transition is accompanied by a concomitant cell-doubling crystallographic structural phase transition. Intriguingly, the cell-doubling transition is featured by a broken inversion symmetry along the axis and a disparity in the CDW-modulation vectors with opposite signs, which gives rise to two sets of CDW domains with reversed contrasts. The profound physics underlining this notable domain-contrast behavior is discussed.