We have something that sounds like what you might want.
The user clicks a link on the web page. This triggers creation of a pdf file using Jasper reports & then starts a download process. The user sees their standard download dialog box & if they select 'open' rather than 'save' it automatically opens Adobe & displays the pdf report.
The key bit of code is:
If this is the behaviour you're looking for, try investigating file download for more info.
By the way, we ran into a problem using the basic JRPdfExporter. If you need to deal with large reports, look into downloading a fix from the jasper sourceforge project called patch.tar.gz. It allows you to use JasperExportManagerStreaming.fillReportToPdfStreaming() instead.