Hi Davulsukur,
Individual segments copy parallel at the same z height, 3d curves or multiple segments are transformed including z, a mode that copies parallel at the same z would presumably be a different kind of transform so would need an enhancment or new feature. You would need to file a Service Request asking for such an enhancement.
It might also be worth checking in the MicroStation Forum to see if anyone there has other suggestions. Copy Parallel is a MicroStation (platform) tool.
How about a custom line style? In the front view below the two copies of the b-spline have been transformed in z, but changing the line style of the original to the (this is quite crude but adequate for demonstation) '{ Rail Road }' line style you can see the parallel rails have the same z-height.
You could create a custom line style at the correct scale and spacing to achieve a similar result, might that do the job?