the "mixed content" warning, at least in firefox, only appears as a little note on the TLS "padlock" icon. I am pretty sure chrome handles things this way too. I wouldn't worry about it. (EDIT: That is to say, the mixed media warning is not a full-page warning the way a self-signed certificate is).
Login pages are a good start, but there are other pages who's content should be not visible to a MITM. For example, administrative pages and / or the Malware Response Forums.
Edited by ScathEnfys, 10 July 2016 - 09:53 PM.