Final answer:
The double-layer sheets of serous membrane that support the viscera are called mesenteries, which are part of the peritoneum in the abdominal cavity.
Step-by-step explanation:
The double-layer sheets of serous membrane that support the viscera are called mesenteries. A serous membrane, or serosa, is composed of a layer of mesothelium supported by connective tissue. These membranes line the body’s coelomic cavities and cover the internal organs within these cavities. Specifically, in the abdominal cavity, the serous membrane known as the peritoneum forms double sheets called mesenteries, which suspend many of the digestive organs. Mesenteries hold the organs in place, containing blood vessels, lymphatic vessels, and nerves that supply the organs, and secrete serous fluid to reduce friction.