Hi Rani,
I have successfully built a 2 level drill report suite (Applications -> Vendors -> Cost Source) and it took a couple of goes before I got it right.
From memory the trick here is to make sure that the "middle report", has keys/granularity that link it to both the first top level report AND the 3rd level bottom report.
In your example, it sounds like Service ID from the Business Service object will be enough granularity. Add this to all of your reports (in the filter section is fine).
When setting up the drill in Apptio between your reports, try changing the filter to be "Filter only on selected column". Having the Service ID in all reports should support the drill functionality and link your data. Apptio is not trying to apply filters being inherited from Report 1 -> Report 2 from the other columns there which probably don't exist in Report 2 -> Report 3. I can't remember if I deselected "Include current report's filters".
Hope you get there with something like this.
Mark
#ApptioforAll