You can't have it all. The HTTP RFC is very clear that referrer data from HTTPS sites should not be sent to HTTP sites (in order to protect the content of the HTTPS site - remember: Even the URL is transmitted in an encrypted way, so it might contain sensitive data).

So by doing the Google searches over HTTPS, you make the life of pages and analytics vendors harder, but you are doing a huge favor to the end users because now their searches are private between them and Google. Nobody else on the way can sniff them. No government and no neighbor/coworker.

Of course, once the user clicked and found your site, the URL the user initially used isn't that confidential any more, so in theory, passing the referrer wouldn't be a problem in this case, but that's not what the standard says and it's not what browsers are doing.

If you want to see this changed, talk to the IETF or the W3C to have the standard changed such that, for example, google could add some rel= attribute to tell the browser that sending a referrer is OK.

Or just serve your page over SSL, further helping the end-user - and it's all about them in the first place - isn't it?