add this line:
famMan.CurrentType = familyType
before this line:
famMan.Set(familyParam, IN[1] + familyType.AsString(familyParam))
your code becomes:
import clr
clr.AddReference("RevitAPI")
from Autodesk.Revit.DB import *
clr.AddReference("RevitServices")
from RevitServices.Persistence import DocumentManager
from RevitServices.Transactions import TransactionManager
doc = DocumentManager.Instance.CurrentDBDocument
param_values = list()
types = doc.FamilyManager.Types
famMan = doc.FamilyManager
TransactionManager.Instance.EnsureInTransaction(doc)
familyTypesItor = famMan.Types.ForwardIterator()
familyTypesItor.Reset()
while (familyTypesItor.MoveNext()):
familyType = familyTypesItor.Current
familyParam = famMan.get_Parameter(IN[0])
param_values.append(familyType.AsString(familyParam))
famMan.CurrentType = familyType
famMan.Set(familyParam, IN[1] + familyType.AsString(familyParam))
TransactionManager.Instance.TransactionTaskDone()
OUT = param_values
-biboy