We have studied the microscopic dynamics of a glass-forming liquid in the soft confinement formed by microemulsion droplets using inelastic neutron scattering. The confined liquid was propylene glycol, the outer, hydrophobic phase was decalin, and the surfactant sodium dioctylsulfosuccinate (AOT) with the same composition used before with other spectroscopic methods [L.-M. Wang, F. He and R. Richert, Phys. Rev. Lett., 2004, 92, 95701]. The inelastic neutron scattering experiments were carried out on several time-of-flight and backscattering spectrometers to cover a large dynamical range. A Fourier transform was used to combine the data in terms of the intermediate scattering function S(Q,t) on a time range from 0.1 ps to 2 ns. By using two isotopic compositions the scattering of the glass-former was separated from that of the matrix liquids. In general we found an acceleration of the glass-transition-related α relaxation in confinement combined with a moderate broadening of the relaxation time distribution. This effect is most pronounced for low temperatures (≤250 K) and fades out at about 270–300 K. In addition, inelastic scattering allowed us to observe the motion of the methyl group of propylene glycol and the vibrational dynamics in the glass. For the methyl group reorientation we also found an acceleration but a narrowing of the relaxation time distribution. The vibrational dynamics show that the glass-typical ‘boson peak’ of bulk propylene glycol is completely washed out in the microemulsion in contrast to all earlier studies using hard confinement, which observed a low-frequency cut-off.