Thermoplastic apparent interpenetrating polymer networks (t-AIPNs) of crystallizable polyurethane (CPU) and a styrene/acrylic acid block copolymer (S-b-AA, acid form) of several compositions were prepared by casting from a common solvent. A variety of experimental techniques, including size exclusion chromatography (SEC), differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), dynamic mechanical analysis (DMA), broadband dielectric relaxation spectroscopy (DRS), thermally stimulated depolarization currents (TSDC), and density measurements were employed to investigate structureproperty relationships of the t-AIPNs. Special attention was paid to the investigation of molecular dynamics of the CPU component in the t-AIPNs, by combination of the dielectric DRS and TSDC techniques, as well as from the methodological point of view, to the prospects of morphological characterization by broadband DRS. The results show that the CPU/S-b-AA t-AIPNs studied can be considered as multiphase systems having at least two amorphous and one crystalline phases, as well as regions of mixed compositions. Their properties are determined by the heterogeneity of the individual components, as well as by the heterogeneity caused by the thermodynamic incompatibility of these components. The degree of incompatibility is determined, to a large extent, by the intermolecular hydrogen bonding between the functional groups of the CPU and the S-b-AA components (ester groups and COOH-groups, respectively), which is more effective on addition of small amounts of either of the components.