In a newborn, higher bilirubin is normal due to the stress of birth. Normal bilirubin in a newborn would be under 5 mg/dL, but up to 60 percent of newborns have some kind of jaundice and bilirubin levels above 5 mg/dL.f bilirubin is not being attached to sugars (conjugated) in the liver and/or is not being adequately removed from the blood, it can mean that there is damage to your liver. Testing for bilirubin in the blood is therefore a good test of damage to your liver.