We apply the methodology and concepts developed over the past years for the study of segmental dynamics on miscible polymer blends to the investigation of a blend made of styrene-butadiene rubber (SBR) and an oligomer of polystyrene (PS) as an example of a simplified industrial system. In this way we obtain detailed information about the segmental dynamics of both components within the blend. To this end, a judicious combination of broad-band dielectric spectroscopy (BDS) and quasi-elastic neutron scattering (QENS) results on deuterium-labeled blends was required. Difficulties on the comparison between isotopically different samples arose due to changes in polymer microstructure associated with the obtention of deuterated polymers. Nevertheless, the strategy for data analysis developed in this work made it possible to readily resolve the components' segmental dynamics of the investigated mixtures. It was found that Gaussian distributions of the components' effective glass-transition temperatures provide a very good description of all the experimental data collected in the SBR/PS (50/50 wt %) mixtures over the whole accessible temperature range, not only by BDS and QENS but also those obtained by differential scanning calorimetry and by neutron elastic fixed window scan experiments.