Joining two red-black trees
Your question surprisingly has an answer on stackoverflow, no doubt dating before this site. The question gives an algorithm of time complexity $O(\max(H_1,H_2))$, and claims that it can be improved to $O(\min(H_1,H_2))$.

By the way, oftentimes $O(H_1 + H_2)$ is used for $O(\max(H_1,H_2))$.