That is what is typically referred to as a Gumby style suit. It is constructed of neoprene foam which provides both insulation and inherent buoyancy. It's traditionally what is worn by pilots flying the North Atlantic route, easily rented from numerous sources at a modest rate, and is rolled down to the waist during flight. Yes, it is awkward to fly in and has significant drawbacks. There's lots of variations of this suit by numerous manufacturers.

Another alternative is the "rubber" suit which is worn with included insulation. The Mustang Survival Ocean Commander is an example of this style. Somewhat better, but still inherently buoyant in some designs and still typically worn rolled down at the waist. Depending upon how it is configured and the insulation chosen, may also require a separate vest for enough buoyancy in the water

The latest technology are Gore-Tex based suits worn with insulation under and a inflatable vest over as they are not inherently buoyant. You can adjust the insulation for the expected conditions. These are the type suits worn by the military and Coast Guard aviation and rescue swimmers.

Some examples are the Switlik U-Zip-It Aircrew Anti-Exposure Flight Suit (this is a PDF file) or the Mutltifabs Aircrew Survival Suits. These are also made by a number of manufacturers with various features. These are worn just like a regular flightsuit (and are very similar in many respects to suits used for kayaking and sailing). These are what I recommend (and what I own), but they are much more expensive than the Gumby suits.