I have exactly the same probleme I'm running Zimbra network edition Version 5.0.15_GA_2851.UBUNTU8.NETWORK on a debian etch.
I have configured zimbra in just https mode (no http) webmail access and others (IMAP, POP, SMTP) works fine.
My problem is just when a user want to change his password on the webmail: a pop-up is open but URL is like this:
http://. It has to be like this https://
I have the same problem in administration when i click on view mail.
Any idear? i have search in configuration with zmpro gacf, gs, gd, ga.