I now realize the question has moved from the cfheader-cfcontent code to the structure of the URL. In my attempt to reproduce the issue, I put the code
<cfheader name="Content-Disposition" value="inline; filename=myReport.pdf" />
<cfcontent type=" application/pdf" file="C:\ColdFusion11\cfusion\wwwroot\workspace\cf11_proj\files\report.pdf" deleteFile="no" />
in the file C:\ColdFusion11\cfusion\wwwroot\workspace\cf11_proj\test\index.cfm. I then ran the following URLs in turn:
http://127.0.0.1:8500/workspace/cf11_proj/test/?someVar=5
http://127.0.0.1:8500/workspace/cf11_proj/test/index.cfm?someVar=5
Both worked as expected, opening the PDF in the browser. I tested on Chrome, Internet Explorer 11 and Firefox 30. I am on Coldfusion 11, and use the built-in web server.