When I import cad I only use the annotation and line (you may need a polygon feature class)
I have two layers set up: the building_labels for the annotation (i have to import manually)
and they AshlandSchoolsFloorplan layer
I position my cad drawing (GS-3.dwg) to a location

In an edit session (I am editing AshlandSchoolsFloorplan)
I then turn off all but the polyline layer.
I select all of the polyline layer.

I hit Ctrl + c then Ctrl + v
I ensure that I am copying to the right layer

Turn off your cad drawing to make sure that the layer copied correctly.
I then will add all building labels from the annotation to the building_labels feature class.
If you need the polygon layer then repeat the steps above on with the Polyline turned off and the Polygon turned on.
I then will remove all cad drawings from the mxd
I then share as service.