You are making two assumptions here:
1. More hash functions equals more security (hash encapsulation)
2. The attacker wants to know the content of 'm'
H0(H1(m)) has the security of just H0. Hashes are not made to protect the content of m, but instead made to test the integrity of m. As such, a flaw in H0 will break the security guarantee, no matter how secure H1 is.
Practically, H0(H1(m)) is the same as H0(m), as m is just "some data," and the result of H1 can be seen as "some data".
If your construction is H0(m0) + H1(m1) where m0, m1 are both halves of m, then the overall security is reduced to the weakest hash function. For example, a length extension attack in the weakest hash function breaks the overall integrity of the construction.