I'm on Coumadin (8mg every day but Tues and Sat, then I take 6mg) for a blood clot in my leg. I personally, have a big problem with soy based products and my INR levels. I try and stay away from anything containing soybean oil because that's very high in Vitamin K, which can effect the PT/INR levels drastically. Anything soy, including soy milk, soy sauce, edamame (the raw form of the soy pod), soybean oil, doesn't agree with me so I try and stay away from it. When I was first diagnosed with the blood clot, I was eating a lot of the Smart Ones frozen meals because they were easy to make, and a week of eating those my blood got way too thick. Come to find out it's loaded with soybean oils, so that's what did it.
Since your husband is lactose intolerant, maybe he could possibly try rice milk or even almond milk? There's also something called oat milk, but I've personally never seen this, I read about it in a health food magazine.
Wishing you the best, and hope you and your husband figure out what is going on.