By default this is how Magento behave.
Try creating a links.phtml file with the following code
if(Mage::app()->getStore()->isCurrentlySecure()){
$url = Mage::getUrl('about-us', array('_secure'=>true));
//$url = Mage::getUrl('',array('_secure'=>true) . 'about-us'; // if above code doesn't work try this
}
else{
$url = Mage::getUrl('about-us');
}
echo '<a title="Click here for more information" href="'. $url .'" target="_self">About Us</a>';
Then in your static block
{{block type="core/template" template="path/to/file/links.phtml"}}
Using apache rewrite will redirect the page to https but the link when viewing source will still be without https
If you have caching enable on your server double check to make sure it doesn't cache one version .... if cached, then you need to change block type (core/template) to one that doesn't cache)