I think it might be easier to explain if you can post a file of what you are starting from.
If you have a planar surface or curves to start with, then you can use the polysurface approach described above to generate a starting mesh with vertices along the shared boundary, then preserve this as a feature curve.
If instead you have some existing meshes from a different source with adjacent boundaries but non-matching vertices then a different approach will be needed (like the one here).