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For a joint program, say a JD/MA, is the tuition rate just the same as the law school or grad school (whichever is higher)? If it doesn't say anything about it on the website, is this safe to assume?

Typically from what I understand it works like this (using a JD/MBA example):

Year 1: Attend law school, pay law tuition
Year 2: Attend business school, pay business school tuition
Year 3: Attend both, pay split tuition based on courseload
Year 4: Attend both, pay split tuition based on courseload

Essentially you pay the law school tuition rate for the time you're in law school and the grad school tuition rate for the time you're in grad school.