I have Jira (Software & Core 7.8.1) running on Windows Server 2012 (IIS 8.5) using the Tomcat IIS Connector (set up following https://confluence.atlassian.com/adminjiraserver071/integrating-jira-applications-with-iis-802593039.html).
HTTPS is configured and working for the most part, however during startup instead of seeing the animated startup screen (which works on standard HTTP) IIS serves a white page stating "The service is unavailable." and throwing a HTTP 503 in the background.
Once the startup is complete, HTTPS responds as normal, displaying the JIRA login screen.
