Final answer:
Splitting on the basement membrane seen on electron microscopy is indicative of Pseudoxanthoma elasticum, an autosomal recessive disease affecting the skin, eyes, and cardiovascular system.
Step-by-step explanation:
The disease associated with splitting on the basement membrane when observed under an electron microscope is Pseudoxanthoma elasticum. This is an autosomal recessive hereditary disease that involves calcification and fragmentation of elastic fibers. Electron microscopy can reveal structural changes in the basement membrane, such as splitting or fragmentation, which are indicative of this condition. Such changes affect multiple systems, including the skin, eyes, and cardiovascular system. This reinforces how powerful electron microscopy is in visualizing ultrastructural changes in various diseases.