We utilize the time-dependent wave-packet propagation method to simulate the complete fragmentation dynamics of ${\mathrm{H}}_2$ molecules subjected to the two-color field. The study focuses on elucidating the influence of the carrier-envelope phase (CEP) difference between the two laser beams on key dynamical properties, including the alignment of neutral molecules, ionization probability, dissociation probability, proton angular distribution, and kinetic energy release (KER). Our study shows that two-color fields can simultaneously provide coherent and incoherent modulations of molecular dynamics. For neutral molecular alignment, two-color modulation proves ineffective as it depends quadratically on intensity rather than wave properties. However, strong-field ionization's inherent nonlinearity enables coherent control through intensity-dependent angular distributions and ionization probabilities. Examining ${\mathrm{H}}_2^{+}$ fragmentation dynamics, we observe coexisting first-, second-, and third-order processes under two-color irradiation. First-order transitions exhibit incoherent modulation via laser component competition, altering vibrational distributions and KER spectra phase independently. The second-order ${\omega }_2-{\omega }_1$ process repopulates bound states but minimally affects fragmentation. Crucially, at high intensities, the dominant third-order ${\omega }_2-{\omega }_1+{\omega }_1$ process enables phase-dependent coherent control through reexcitation of second-order-created bound states, revealing fundamental insights into multiorder process interplay in strong-field molecular dynamics.

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• Molecular dissociation
• Ab initio molecular dynamics