Miscible S-SBR (solution styrene-butadiene copolymer)/BR (polybutadiene homopolymer) blends are used in multiple applications like modern passenger car tire treads. Despite their miscibility, there is a problem to predict tire performance due to dynamical heterogeneities present in the S-SBR/BR blends. On the one hand, S-SBR/BR blends have a thermorheologically complex behavior, which complicates the prediction of the temperature- and frequency-dependence of material properties. On the other hand, due to differences in the polarity of the individual components, the extender oils used in the elastomeric compounds could distribute unequally within the blends, where little is known about how oils interact with the two polymers. In this work a combination of Differential Scanning Calorimetry, Dynamic Mechanical Analysis, and Broadband Dielectric Spectroscopy (BDS) is used to clarify: (i) the thermorheological complexity of S-SBR/BR blends, (ii) the effect of the extender oil on the blend. The broad frequency operation of BDS allows for the analysis of the S-SBR and BR component dynamics and the effect of the oil on each of them within an S-SBR/BR (50/50) blend. Based on the discretization of individual component dynamics in the blend, conclusive remarks are made on the effect of the extender oil for either component in the blend.