Chrome definitely complains as well. It puts up the red skull and crossbones and crosses out the https in the address bar. It doesn't pop up anything though.
I think you may have visited a page that's not intended for https via https, then went to the https page and the domain is flagged in Chrome for the session. This is a known issue with Chrome. It wouldn't occur for most users... try clearing your sessions or reopening chrome and browsing the site regularly.