You can be enrolled in two schools at once but only one school can receive the loans. That school has to pay the other school or reimburse you so you can directly pay the separate tuition.
How are you figuring that it would be cheaper for you?
It’s hard for me to imagine many scenarios in which attending two separate schools would be cheaper because you would have to pay both Michigan and Mizzou concurrently. Whereas, within the same institution, you’re typically not paying both DVM and MPH tuitions concurrently.
At Ohio State, DVM/MPH students pay just vet school tuition in the Spring and Fall semesters, even when taking MPH related credits, and just MPH tuition for credits related to that program in the summer or in any semester they are singly enrolled. It’s that way across campus for any dual degree student too (DVM/MS, MD/MHA, MD/JD, etc.). I doubt OSU is unique in its handling of dual degree students.