Ajax using https on an http page
Add the Access-Control-Allow-Origin header from the server
Access-Control-Allow-Origin: https://www.mysite.com
Try JSONP.
most JS libraries make it just as easy as other AJAX calls, but internally use an iframe to do the query.
if you're not using JSON for your payload, then you'll have to roll your own mechanism around the iframe.
personally, i'd just redirect form the http:// page to the https:// one
http://example.com/ may resolve to a different VirtualHost than https://example.com/ (which, as the Host header is not sent, responds to the default for that IP), so the two are treated as separate domains and thus subject to crossdomain JS restrictions.
JSON callbacks may let you avoid this.