We're publishing our Revit data to DGN format using the Revit I-model plugin. We then reference that i-model into a new empty DGN file, merge the reference, then apply a Family and Part to the merged elements. After creating Drawing Views from these elements they do not seem to honor any of the Family and Part resymbolization, such as section plane hatch/patterning.
Unfortunately i-model elements will not work with Family and Part resymbolization since that system was designed to accommodate Forms and Solids. You would see the same results if you were to take two walls with no Family and Part assigned, add them to a cell, and then apply a Family and Part to the cell itself. Although different than the Type 106 elements created through the i-model process, the end result is the same since the base element is not a Form or Solid.
If you do need to use Revit data in this context, the better route would be to use IFC instead. This will generate geometry that works as expected with Family & Part resymbolization.