Indeed. Meet the Miller family -
http://edventureproject.com/wordpress/?page_id=3 ("We spent a year touring most of Europe and part of North Africa on our bicycles… with all four kids")
Or the Vogel family - http://familyonbikes.org/blog/?page_id=10 ("The Vogel family left June 8, 2008 for a 2 1/2 year bicycle trip traversing the Pan-American Highway from Alaska to Argentina.")
It can be done.
