Bilayers composed of Co and Cu were prepared on MgO(111) substrates as a fundamental unit of the superlattice of Cu and Co; the dependence of the crystal structure of each elemental layer on the thickness was investigated by reflection high-energy electron diffraction (RHEED) observation and X-ray diffraction (XRD) analysis. When Co was deposited first on MgO(111), it exhibited an f.c.c. structure for layers up to 30 nm thick and changed to an h.c.p. structure with increasing Co thickness; subsequently deposited Cu exhibited an f.c.c. structure regardless of the crystal structure of the underlying Co (f.c.c. or h.c.p.), Cu on MgO( 111) had an f.c.c. structure, and Co on f.c.c.-Cu/MgO(111) exhibited a mixed structure of f.c.c. and h.c.p. phases for a 5 nm thick layer and an h.c.p. structure for a 100 nm thick layer.