In the course of my studies I have encountered several differing points of view on the subject. In his book on liver therapy, Christopher Hobbs states that bitter tonics should be taken 15 minutes to 1/2 hour between meals. Dr. Vasant Lad gives general ayurvedic guidelines that herbs working on the lower part of the body such as purgatives, diurectics and emmenogogues (think colon, bladder and uterus) should be taken before meals; herbs that work on the digestive function such as stimulants, carminatives, bitter tonics and nutritive tonics (think stomach, spleen, liver and small intestine) should be taken with meals; herbs that work on the upper body such as diaphoretics, expectorants, nervines (think lungs, heart, brain) should be taken after meals.
That being said, what I have found for myself and my family and friends is that unless you have very strong digestion, bitter liver herbs can disrupt the digestion unless you take enzymes or digestive herbs with them. Especially if you take a lot of the liver herbs as is recommended for healing a truly toxic liver.
One's digestion is usually not strong when the liver is ailing.
Everybody is different. You can try taking the milk thistle with your meal and see if you feel any disruption, such as feeling a bit bloated or getting gas/belching after eating. If your digestion does feel sluggish with the milk thistle you can try digestive enzymes with it, or try taking it before or between meals to see what works best for you.