I tried to reproduce the problem you described with referencing an image from file system from within a Content Block. It worked fine for me. What I did:
1. Go to Administration->Files.
2. Create a folder "images" in the root folder.
3. Upload an image "tulips.jpg".
4. Go to Pages and create a new page.
5. Inserte a Content Block and click "Enter content" to edit its properties.
6. In the Edit dialog switch to HTML and insert an <img src="~/images/tulips.jpg" /> tag. (screenshot attached)
7. Save the Edit dialog - the image appears in the page editor.
8. Publish the page. Then "View" from the Pages grid - the image also appears fine in the frontend.
Is this what you are doing? If not, please provide us with exact steps or a video so that we can reproduce the problem. I tested with Firefox and IE - both worked fine.
Note: the "src" attribute really gets replaced with an absolute path of the image, based on the virtual path of your application. This is normal, since the browser does not understand application-relative paths, e.g. paths starting with "~/".