No, in humans (and animals, I think) the diaphragm is located just below the lungs.
diaphragm
it is called the diaphram.
At the bottom of the lungs
The diaphragm is shaped like a dome and curves to the bottom of the chest cavity and right above the stomach.
the diaphragm is the muscle separating the chest and the abdomen
The diaphragm is the muscle separating the abdomen from the chest
The chest cavity is where your heart, lungs, and esophagus reside. It's essentially everything located behind the chest wall, but in front of the spine, above the diaphragm and below the throat.
The diaphragm (a sheet of muscle underneath the ribcage) and intercostal muscles (located between your ribs).
diaphragm
Your lungs are in the thoracic cavity, which includes the chest down to the diaphragm. The lungs are located on both sides of the heart in pleural cavities.Source:http://www.dummies.com/how-to/content/what-is-in-the-thoracic-cavities.html
The diaphragm separates the chest from the abdomen and pelvis
the diaphragm, chest muscles, ribs and the sternum.