We have combined X-ray diffraction, neutron diffraction with polarization analysis, small angle neutron scattering,differential scanning calorimetry, and broad band dielectric spectroscopy to investigate the structure and dynamics of binary mixtures of poly(2-(dimethylamino)ethyl methacrylate) with either water or tetrahydrofuran (THF) at different concentrations. Aqueous mixtures are characterized by a highly heterogeneous structure where water clusters coexist with an underlying nano-segregation of main chains and side groups of the polymeric matrix. THF molecules are homogeneously distributed among the polymeric nano-domains for concentrations of one THF molecule/monomer or lower. A more heterogeneous situation is found for higher THF amounts, but without evidences for solvent clusters. In THF-mixtures, we observe a remarkable reduction of the glass-transition temperature which is enhanced with increasing amount of solvent but seems to reach saturation at high THF concentrations. Adding THF markedly reduces the activation energy of the polymer β-relaxation. The presence of THF molecules seemingly hinders a slow component of this process which is active in the dry state. The aqueous mixtures present a strikingly broad glass-transition feature, revealing a highly heterogeneous behavior in agreement with the structural study. Regarding the solvent dynamics, deep in the glassy state all data can be described by an Arrhenius temperature dependence with a rather similar activation energy. However, the values of the characteristic times are about three orders of magnitude smaller for THF than for water. Water dynamics display a crossover toward increasingly higher apparent activation energies in the region of the onset of the glass transition, supporting its interpretation as a consequence of the freezing of the structuralrelaxation of the surrounding matrix. The absence of such a crossover (at least in the wide dynamic window here accessed) in THF is attributed to the lack of cooperativity effects in the relaxation of these molecules within the polymeric matrix.