If I have a Will, does my family avoid probate?

Not necessarily.  Probate is a court proceeding that manages and settles your estate.  If there is property to be administered or taxes to be paid, the existence of a Will does not necessarily avoid probate nor does it increase the expense of the probate process.  A Will is basically a road map or set of instructions for the court.  However, if all of your property is held jointly or in trust probate may not be necessary after your death.  Probate is not necessarily a process to avoid.