What happens when you put Portal into "Allow access to the portal through HTTPS only."
I believe without that setting, most pages that do not require HTTPS (such as login) will redirect to HTTP.
Perhaps the following will spark an idea:
I have had an issue with a problem that is sort of the reverse of this.
I was in Allow HTTPS only mode and turned it off.
Portal then would redirect to HTTP for most of the web pages but I kept getting an error that HTTPS was required.
In that situation, my IIS SSL settings were set to SSL Required. I turned it off and was back to a mixed mode Portal that worked as expected.