Double-crystalline diblock copolymers of linear polyethylene (LPE) and hydrogenated polynorbornene (hPN) are synthesized, and their crystallization behavior and morphology are examined using small-angle (SAXS) and wide-angle X-ray scattering (WAXS). In symmetric hPN/LPE diblocks with molecular weights above 50 kg/mol, the hPN block has previously been shown to crystallize first and set the solid-state microstructure. Two-dimensional WAXS on hand-drawn fiber specimens reveals that the LPE crystals formed in confinement stack orthogonally to the hPN crystals. By adjusting total molecular weight, the order of block crystallization may be reversed, even while holding the block length ratio fixed. At a diblock molecular weight of 20 kg/mol, simultaneous time-resolved SAXS/WAXS reveals that the LPE block crystallizes first, even when LPE is the minority component, and restricts hPN to crystallize between the LPE lamellae. The relative orientation of the LPE and hPN crystals in the lower molecular weight diblocks is examined by modeling changes in the SAXS primary peak intensity on cooling two diblocks through the hPN crystal-crystal transition, where hPN densifies as it adopts a rotationally ordered crystal structure. Only a perpendicular stacking of hPN and LPE crystals consistently yields the large reduction in primary SAXS peak intensity observed for both diblocks. Thus, even though the templating block switches from hPN to LPE as the diblock molecular weight is reduced, the orthogonal stacking motif is retained for both high- and low-molecular-weight copolymers.