HTTPS failed to load icons from JQuery API

I put CSS of jQuery UI 1.8.4 downto my site source code, with its images folder along.

In the default page (wrapping page), jQuery CSS is initialized by declaration:

<link href="//Css/App.SrsWPSite/jquery-ui-1.8.4.custom.css" rel="stylesheet" type="text/css" />

My jQuery accordion is set up as usual:

$('SomeId').accordion({ header: '.menuItem', icons: { 'header': 'ui-icon-circle-plus', 'headerSelected': 'ui-icon-circle-minus' } });

It works normally in HTTP mode (CSS loaded successfully).

But, in HTTPS mode, all jQuery accordion icons (and some other css formats) were unable to be loaded.

Taking examination, I found out that they had image url the same to HTTP mode's:

url("http://mypath//Css/Site/images/ui-icons_0078ae_256x240.png")

If I let my site run binded under both HTTP (with default port 80) and HTTPS, then it's OK ! But for sure, I just want to force my site to run under HTTPS mode.

I also tried to use MS Url Rewrite, but it brought no use.

Is anybody willing to help me by your experience ? Thanks