Therapeutic proteins are usually conserved in glassy matrixes composed of stabilizing excipients and a small amount of water, which both control their long-term stability, and thus their potential use in medical treatments. To shed some light on the protein-matrix interactions in such systems, we performed molecular dynamics (MD) simulations on matrixes of (i) the model globular protein lysozyme (L), (ii) the well-known bioprotectant trehalose (T), and (iii) the 1:1 (in weight) lysozyme/trehalose mixture (LT), at hydration levels h of 0.0, 0.075, and 0.15 (in g of water/g of protein or sugar). We also supplemented these simulations with complementary inelastic neutron scattering (INS) experiments on the L, T, and LT lyophilized (freeze-dried) samples. The densities and free volume distributions indicate that trehalose improves the molecular packing of the LT glass with respect to the L one. Accordingly, the low-frequency vibrational densities of states (VDOS) and the mean square displacements (MSDs) of lysozyme reveal that it is less flexible-and thus less likely to unfold-in the presence of trehalose. Furthermore, at low contents (h = 0.075), water systematically stiffens the vibrational motions of lysozyme and trehalose, whereas it increases their MSDs on the nanosecond (ns) time scale. This stems from the hydrogen bonds (HBs) that lysozyme and trehalose form with water, which, interestingly, are stronger than the ones they form with each other but which, nonetheless, relax faster on the ns time scale, given the larger mobility of water. Moreover, lysozyrne interacts preferentially with water in the hydrated LT mixtures, and trehalose appears to slow down significantly the relaxation of lysozyme-water HBs. Overall, our results suggest that the stabilizing efficiency of trehalose arises from its ability to (i) increase the number of HBs formed by proteins in the dry state and (ii) make the HBs formed by water with proteins stable on long (>ns) time scales.