Can scholarship money cover cost of living/books/housing?

It depends on several factors. First, each school has rules on how much scholarship money a student can receive. At some schools scholarships (both school awarded and outside combined) cannot exceed the cost of tuition. In the case that you receive a school awarded scholarship and another outside scholarship that exceeds tuition costs then your school award will be reduced.
Some schools offer a very limited number of full-tuition fellowships that include an additional stipend. Consideration for these awards will differ by school (i.e. requiring an additional application or not).
The biggest factor in determining if outside scholarship money can be used for living expenses is if the money goes to the student or the university. Some scholarships are sent directly to the school while others go to the student. If the money goes to you then you typically can use it as needed to cover books, student fees, and living expenses, if needed. These awards are great for students who have a full-scholarship but are looking to offset the additional costs beyond tuition.

Hope this helps.

I agree with everything cheetarah1980 has said, another important factor is your location even if you're getting Scholarship. Obviously, in big cities the cost of living is higher and it drains your financial resources a lot more. On the flip side, sometimes you don't have to invest for travelling to career fairs (usually organized in big cities) and you can save some Money there.
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If you manage to get $60k+ in scholarships let me know where all you applied because that would be a pretty nice deal.

Is this the way it is with all MBA programs? I, and a few friends, had scholarships that covered all living expenses in med school.

I can't speak for all MBA programs. I only attend one. I remember a bit of stuff from the other schools I got into, but I wouldn't extrapolate that to all schools. Some schools do have a few fellowships that offer full-tuition plus a 10-20K/year stipend. However, they aren't many so I wouldn't depend on one coming through for you. If it does, then that's a beautiful bonus.