I successfully merged this mod with Enhanced UI v1.21beta1. I believe it should also be fully compatible with EUI 1.20.
Requires both EUI and Health and Plague, and does not actually replace either in full.
https://www.dropbox.com/s/8fuua14nierb2b0/EUI v1.21beta1 - Health & Plague V7 - MERGE - V1.rar
Just grab that, and copy it into your Health and Plague folder, overwriting when prompted.
By extension, this also increases compatibility with City-State Diplomacy.
I also made another version that, in addition to the above merge, also merges with Emigration:
https://www.dropbox.com/s/loi4vaf8z...tion V5 - Health & Plague V7 - MERGE - V1.rar
NOTE: The Emigration merge will also require you to install my EUI-Emigration merge, which is still a bit buggy, and can be found here:
http://forums.civfanatics.com/showpost.php?p=13287568&postcount=376