The nuclear magnetic resonance (NMR) and dielectric spectroscopy (DS) methods were used to investigate the segmental and global dynamics in lamellar microphase separated poly(styrene-b-isoprene) (SI) diblock copolymer. For the first time, the susceptibility representation of the NMR relaxation data is applied to the analysis of the molecular dynamics in complex polymer systems like the diblock copolymer. This approach in combination with the frequency-temperature superposition (FTS) allows one to compare directly the NMR and DS data in an extended frequency range providing a unique comprehensive picture of various relaxation processes present in the system studied. The findings of these investigations include structural relaxations of the polyisoprene (PI) and the polystyrene (PS) blocks, a normal mode relaxation of the PI block, and an extra low frequency interfacial relaxation. Special attention has been devoted to influence of the copolymer morphology on the segmental and global dynamics in PI.