That's not what it's doing for me-ie7 or ie8 at work, FireFox can't be bothered to stand up and check version on laptop, and the browser on my phone. Doesn't massively bother me except it really really didn't play nice with the proxy server in one site which gets grumpy about https.
Hmm, that's odd. I'm not 100% what's going on, but I guessed it was slightly different headers being sent back to the browser depending on what protocol was being used, which sometimes caused the browser to reload the page.
IE7 on this Windows XP box doesn't re-request the page when you return to the http page, and Firefox on this box, and on my Ubunut-derived distro at home also works like this.
Possibly it could be the effect of Proxies between you and the server.