Time-resolved simultaneous synchrotron small-angle X-ray scattering and differential scanning calorimetry experiments have been performed on crystallization of polyethylene-polyisoprene diblock copolymers (HEI or LEI) and their blends with corresponding homopolymers, polyethylene (PE) and polyisoprene (PIp). For the neat block copolymer having a 50 wt% of the crystalline component, preexisting microphase separation structure in the melt was kept at high and low crystallization temperatures T_c (T_c≥94°C and T_c<60°C), while disrupted at intermediate T_c (60°C≤T_c<94°C). This complex behavior was interpreted by combination of two mechanisms. The behavior in the crystallization below 94°C was attributed to the competition between the crystallization and chain diffusion rates, that is, the fast crystallization rate at lower T_c makes it difficult to rearrange the phase structure in the melt. On the other hand, at a higher T_c (≥94°C), the preservation of the microphase separation structure was explained by a small degree of crystallinity due to the ethyl branch of polyethylene (hydrogenated poly(butadiene)). For HEI/PE blends, crystallization behavior was the simple superposition of those for HEI and PE, while, for HEI/PIp with a small composition of PE, suppression of crystallinity was observed. Crystallization kinetics in the neat block copolymer and all the blends was not so different from that in the PE homopolymer.