What you are asking for is the two-volume The Babylonian Gilgamesh Epic by A. R. George. This masterful work includes the editions of all of the known tablets of the Gilgamesh epic (except for the most recenly discovered tablet), an English translation, and images of the cuneiform tablets. These aren't side-by-side like the Loeb Classical texts, but it's the best you will be able to find. The set is expensive, so you will likely need to find an academic library in order to use it. It also may not be suitable for non-specialists. The work was published mainly with Assyriologists in mind, so if you cannot read Akkadian, looking at the editions and the tablets won't be of much help.