Hi carolinc... No, I don't think this diet does sound healthy. It only centers on protein and I'm afraid it might be very lacking in nutrients. The body needs a wide variety of nutrients, other than protein.
I see nothing that indicates your husband would be eating vegetables, fruits, meats or anything that would be providing the calcium, vitamins and other minerals his body needs. Yes, I know, many protein shakes have added vitamins and minerals, but they often don't contain everything we need to stay healthy...
It's also not something that can be maintained over the long term, so once the weight is lost, then what? If one does not develop healthy eating habits, chances of regaining lost weight, often, plus some, are very great and can result in yo-yo dieting... Please note the title of the article "What is the fastest way to lose fat - don't care if it's ethical"...or safe to diet like that...
Try to convince your husband to implement a diet that consists of lean protein in the form of meats, eggs and legumes, along with a wide variety of colorful veggies and fruits, healthful fats, etc in the amounts he needs for his own body, based on his current age, weight and height, with reasonable exercise. By doing this, he can make lifestyle changes and come up with a plan that he can stick with in order to stay healthy for life, not just a quick fix.
Please post back and let us know how we can further help you.