Inside the cell they are broken into amino acids that then enter the capillary. Gluten enteropathy is the inability to absorb gluten, a protein found in wheat. Digested fats are not very soluble. Bile salts surround fats to form micelles that can pass into the epithelial cells. The bile salts return to the lumen to repeat the process.
Bile salts are in turn absorbed in the ileum and are recycled by the liver and gall bladder.
Fats pass from the epithelial cells to the small lymph vessel that also runs through the villus. Image from W.H. Freeman and Sinauer Associates, used by permission. The liver sends bile to the small intestine. Bile contains bile salts, which emulsify fats, making them susceptible to enzymatic breakdown. Images from W.H. Freeman and Sinauer Associates, used by permission.