We report results on the linear viscoelasticity (oscillatory shear in the temperature range T-g(glass-transition temperature) less than or equal to T less than or equal to T-g+ 90 K) of miscible blends of polystyrene (PS) and poly(vinyl methyl ether) (PVME) and segmental relaxations, measured by dielectric spectroscopy. The Flory-Huggins interaction parameter of this blend is weakly negative, and the glass transitions of the pure components are quite disparate (Delta T-g = 125 K). PS/PVME blends have been found to be consistently thermorheologically complex at both the segmental and terminal levels: the empirical time-temperature superposition (tTS) principle applies to neither their oscillatory shear response nor their dielectric response. Using the tube model, we quantitatively compare dielectric and mechanical results. At low temperatures, the effective time scale for motion of a Kuhn segment (the shortest Rouse mode) is near the long-time end of the distribution of segmental relaxation times of PVME, in both the pure and blended states. The slowest relaxing segments thus control the longer-time relaxation processes of the chains. Miscible blends with weak interactions and large Delta T-g have concentration fluctuations that broaden the distribution of segmental relaxation times. This distribution narrows as the temperature is raised in the blend, leading to the failure of tTS for terminal dynamics.