I'm running Widows 2008 EE with IIS 7. I'd like to setup a reverse proxy with the SSL terminating on my Windows box, then proxying HTTP connections to a mix of IIS and Apache machines internally. So, to clarify (where -> means "proxied to"):
https://www.mydomain.com/svn -> http://myinternalsvnsrv/svn
https://www.mydomain.com/redmine -> http://myinternalredminesrv
etc...
Ideally, I wouldn't use any third-party add-ins like UrlRewriter. Is this possible with only IIS7?
Yes; see Reverse Proxy with URL Rewrite v2 and Application Request Routing.
I can confirm that crb's comment is correct.
I now have redmine and svn both served up using his suggestion. Works a charm. My arrangement is using subdomains, e.g. ://redmine.domain.com and ://svn.domain.com, but either will definitely work.