How to reduce MaxUNSAT to MaxSAT?
Both MaxSAT and MaxUNSAT are NP-complete, and so can be reduced to one another. MaxSAT is NP-hard by (trivial) reduction from SAT. To see that MaxUNSAT is NP-hard, we follow Creignou [1] and reduce from MaxCUT. Given an instance $G=(V,E)$ of MaxCUT, consider the instance
$$ \bigwedge_{(x,y) \in E} (x \lor \lnot y) \land (\lnot x \lor y). $$
Each cut corresponds to a $0/1$ assignment to the vertices. If an edge $(x,y)$ is separated by a cut, then one of the two corresponding clauses will be unsatisfied, and otherwise none will be unsatisfied.

[1] Creignou, A dichotomy theorem for maximum generalized satisfiability problems, JCSS 51, 511-522 (1995).