What can pass through the intestinal membranes?
Virtually all nutrients from food can be absorbed into blood through the lining of small intestine and colon.

What can be absorbed in the small intestine:


Water
Simple sugars (monosaccharides): glucose, fructose, galactose...
Amino acids and small peptides (dipeptides, tripeptides)
Free fatty acids, monoglycerides and cholesterol
Minerals: sodium, potassium, iron, etc.
Vitamins
Nucleic acids
Alcohol
Various other substances from food (polyphenols, sulfate, oxalate, caffeine, preservatives...)
Bile acids
Steroid hormones, such as cortisol, aldosterone and sex hormones (JCEM)
Drugs
Various toxins


What can be absorbed in the colon:


Water
Short-chain fatty acids (from bacterial fermentation of dietary fiber and sugar alcohols)
Sodium, potassium and some other electrolytes 


What cannot be absorbed in the intestine:


Polysaccharides (such as starch), oligosaccharides, disaccharides
Dietary fiber (soluble fiber can be fermented and the resulting substances can be absorbed in the colon)
Whole proteins and big peptides
Triglycerides, diglycerides
Peptide hormones, such as insulin, glucagon, calcitonin, prolactin, growth hormone and parathyroid hormone (Cambridge Core)


Sources:


Lumenlearning (type of transport for all main nutrients)
Best Practice &amp; Research: Clinical Gastroenterology (detailed description with carriers involved)