TYPO3 Core

You can use config.absRefPrefix or config.baseUrl with a proper schema. TYPO3 has no way to determine reliably when the site is http or https. So you have to tell that directly. Some pages can be forced to http or https but that does not apply to subpages. The only we can fix is that forced http/https.

We are using config.baseUrl, this does not help though. The preview link in the backend starts with https:// regardless of the baseUrl.
It must be possible to recognize a "preview" request from the backend and add accordingly: for instance not cache the page if it is a preview request, or delete it afterwards from the cache.
http://old.nabble.com/HTTPS-Backend--%3E-HTTP-Frontend-td32493228.html
discusses the same problem, unfortunately in German.
A different approach might be to correctly generate the preview link in the backend, it should not be https if the actual site is not running on https.

Yes we do have a public DNS Entry.

We can not set absRefPrefix since it does not work with realurl:

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There is a TypoScript-setup directive to set an absolute prefix to all links and images (config.absRefPrefix), but sadly enough that isn't implemented in all places (the indexed-search and front-end-editing for example), so that doesn't work too well.
Please don't use config.absRefPrefix. It has some nasty properties that render RealURLs complete unusable sometimes. The only problem is that the 404-page of TYPO3 doesn't have the <base>-tag, so it doesn't show the TYPO3-logo Support for this might be allowed when the bugs are fixed but generally it will require all code generating reference to use this method and that cannot be guaranteed for all extensions of course.
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Stefan

config.absRefPrefix does work with realurl and Dmitry (the maintainer) even recommends it.
Can you please tell me the chapter of the realurl manual that you copied the above paragraph from?

With domain record, I meant the record inside TYPO3 CMS.

Yeah we do set domain records for every domain we use (It is a rather large site).

http://wiki.typo3.org/Realurl/manual#config.absRefPrefix

Maybe you should use the real manual and not some version by random people in the wiki.
http://docs.typo3.org/typo3cms/extensions/realurl/1.12.6/#config-absrefprefix

Hint: Never trust contents in a wiki!

Anyway, can you please try if this work for your now?

We tried it and I can confirm that it does work. So you were right, the wiki was outdated. This is sometimes hard to see then googling for a solution.
Thanks !