Is there a way to keep a copy of our highlighting in iBooks? (email it or print it)
Can I print my books and PDFs from iBooks?
  
  Yes, you can print PDFs and notes you've entered from iBooks, but the
  option to print ePub books is not available.2 You can also email PDFs
  and notes you have written from iBooks.
  
  Can I highlight text and make notes?
  
  iBooks includes built-in Highlight and Note features. Highlight any
  word or passage of text within a book. You can also create a Note from
  your highlighted selection. Review your Highlights and Notes by
  tapping the Table of Contents button and then tapping Bookmarks.
  Highlights and Notes appear in their own section under Bookmarks.


source: apple support page
Doesn't seem to be a straight yes/no answer for printing of the highlighted area, but you can turn a highlighted area into a note, which will print/email.