We examine the crystallization behavior of polyethylene-b-poly(vinylcyclohexane) diblock copolymers, E/VCH using a combination of transmission electron microscopy (TEM), dilatometry, and time-resolved small-angle X-ray scattering (SAXS). The glassy VCH matrix effectively restricts E crystallization to within the spheres, cylinders, gyroid channels, or lamellae formed by microphase separation in the melt. The VCH matrix can contract in response to crystallization of the E microdomains, so crystallization proceeds without cavitation. The crystallization kinetics strongly reflect the connectivity of the E microdomains: homogeneous nucleation and first-order crystallization kinetics for spheres or cylinders of E; conventional sigmoidal kinetics for the highly interconnected gyroid structure. Lamellar materials show an interesting two-step crystallization behavior: at higher temperature, heterogeneous nucleation permits the crystallization of lamellae interconnected through grain boundaries or defects, and then at lower temperature homogeneous nucleation permits the crystallization of the remaining isolated lamellae.