Reply To: Inserting characters after some Char Style

You have more options to make offsets if you use Paragraph Rules or Paragraph Shading (found under Paragraph Style Options), rather than Underlines. They should provide you with the results you’re looking for.

If just shading behind a single line of text (rather than a whole paragraph) try Paragraph Rules with these options:
for Width: select Text; for Right and Left Indent: make that a negative number like -.05 in