I'm not sure if I completely understand the question, but I believe you could create the stacked bar chart by removing Measure Names from the Columns shelf (on the Side-by-Side Bar Chart).
You're absolutely right about how to create stacked bar chart. Thank you!
But moreover I would like to place labels of percentage on those bars. You may see enclosed workbook how it should look like (a couple of calculated fields added). But in this case percentage labels are duplicated and placed not only on corresponding bars.