To restate what you are saying, you have 1 measure that you want to be able to show as 3 separate lines in a line graph? You could create 3 separate measure fields:
IF YEAR([DateField]) = 2010 THEN [Measure] ELSE NULL END
IF YEAR([DateField]) = 2011 THEN [Measure] ELSE NULL END
IF YEAR([DateField]) = 2012 THEN [Measure] ELSE NULL END
Then, drag the Measure Values field onto the Rows Shelf and turn off all measures but these 3. Put your [DateField] on the columns shelf and set it to show Month (as a discrete dimension--make sure the pill is blue). This will force the lines to overlap. (If you bring year into the Columns shelf, they will NOT overlap.)
If that does not get you what you need, please post a packaged workbook with your example.
Thanks a lot , the solution which you gave is working perfectly fine.