Single crystalline epitaxial Co/Mn superlattices have been grown on a (0001) Ru buffer layer onto mica substrates. The evaporation of a seed layer of 6 angstrom Mn is necessary to obtain a high-quality epitaxial growth. Reflection high-energy electron diffraction, x-ray diffraction, and ferromagnetic resonance experiments clearly show a modification of the Mn structure, when the thickness of the Mn interlayer increases. The Mn structure switches from a compact phase close to the fcc Mn-gamma for few atomic planes, to a less compact one, probably a Laves phase (MgCu2) which resembles Mn-alpha, for larger thicknesses of Mn. This behavior induces a variation of the structure in the Co layers where the stacking changes from fcc to hcp. Up to six Mn atomic planes, the Mn layers being highly strained, the stabilization of the fcc Mn and Co metastable structures occurs via elastic and chemical interactions. For larger Mn thicknesses, there is a trade-off between reduced strains and a higher density of epitaxial dislocations, leading to a lower coherence between the Mn and Co layers. This leads the Mn and Co to approach their bulk structure, Mn-alpha and hcp, respectively. However, the chemical interactions between Co and Mn favor the fcc Co stacking and consequently create a large density of stacking faults in the hcp Co, even when the Mn is no longer close packed.