The self-assembly and the dynamics of an H-shaped copolymer composed of a polyethylene midblock and four poly(ethylene oxide) arms (PE-b-4PEO) are investigated in the bulk and under severe confinement into nanometer-spaced LAPONITE clay particles by means of small- and wide-angle X-ray diffraction (SAXS, WAXS), differential scanning calorimetry (DSC), polarizing optical microscopy (POM), rheology, and dielectric spectroscopy (DS). Because of the H-shaped architecture, the PE midblock is topologically frustrated and thus unable to crystallize. The superstructure formation in the bulk is dictated solely by the PEO arms as inferred by the crystallization/melting temperature relative to the PEO homopolymer. Confinement produced remarkable changes in the interlayer distance and PEO crystallinity but left the local segmental dynamics unaltered. To reconcile all structural, thermodynamic, and dynamic effects, a novel morphological picture is proposed with interest in emulsions. Key parameters that stabilize the final morphology are the severe chain confinement with the associated entropy loss and the presence of interactions (hydrophobic/hydrophilic) between the LAPONITE and the PEO/PE blocks.