The addition of molecular liquid cosolvents to choline chloride (ChCl)-based deep eutectic solvents (DESs) is increasingly investigated for reducing the inherently high bulk viscosities of the latter, which represent a major obstacle for potential industrial applications. The molar enthalpy of mixing, often referred to as excess molar enthalpy HE-a property reflecting changes in intermolecular interactions upon mixing-of the well-known ChCl/ethylene glycol (1:2 molar ratio) DES mixed with either water or methanol was recently found to be of opposite sign at 308.15 K: Mixing of the DES with water is strongly exothermic, while methanol mixtures are endothermic over the entire mixture composition range. Knowledge of molecular-level liquid structural changes in the DES following cosolvent addition is expected to be important when selecting such pseudo-binary mixtures for specific applications, e.g., solvents. With the aim of understanding the reason for the different behavior of selected DES/water or methanol mixtures, we performed classical MD computer simulations to study the changes in intermolecular interactions thought to be responsible for the observed HE sign difference. Excess molar enthalpies computed from our simulations reproduce, for the first time, the experimental sign difference and composition dependence of the property. We performed a structural analysis of simulation configurations, revealing an intriguing difference in the interaction modes of the two cosolvents with the DES chloride anion: water molecules insert between neighboring chloride anions, forming ionic hydrogen-bonded bridges that draw the anions closer, whereas dilution of the DES with methanol results in increased interionic separation. Moreover, the simulated DES/water mixtures were found to contain extended hydrogen-bonded structures containing water-bridged chloride pair arrangements, the presence of which may have important implications for solvent applications.