The primary mechanism for integration with Jazz-based applications (including integrations between the Jazz-based applications themselves) are the open community-defined OSLC APIs, defined at open-services.net .   So someone would need add support for the appropriate OSLC APIs to the Atlassian tools, in order for the Atlassian tools to integrate with the Jazz-based applications.   Tasktop (www.tasktop.com) provides support for some of the OSLC APIs for Atlassian Jira and Atlassian Service Desk.