When the HTML editor inserts images, it generates the following HTML:
< img src="/Portals/0/SomeImage.jpg" />
This HTML will work fine on your site, but it will not work in email.
The problem with this HTML is that it does not include the domain name. In order to fix this, you will need to go into HTML mode and edit the HTML to include the domain name. It should look like this:
< img src="http://www.YourDomain.com/Portals/0/SomeImage.jpg" />