HTML Editor wont insert the Full URL automatically, you would need to edit the image source code using the source button to add the domain to the image source.
You need to edit the image source manually for this.
Your friends over here at WebAssist! These Dreamweaver extensions will assist you in building unlimited, custom websites.
These out-of-the-box solutions provide you proven, tested applications that can be up and running now. Build a store, a gallery, or a web-based email solution.