When deciding which minions to have in your party, think of the Elements as one of the three essential Strategic Points (along with Statistics and Skills). (This was useful to figure out the 'Titan-Titan' effectiveness.) It's not been determined, however, whether this actually alters the healing output. For examples, if you heal a Fire type with a Water skill, the message "Not Effective" will be displayed (water on fire, that's no good, even for healing.) or if you have your Holy type minion healing itself with a Holy skill, the message "Super Effective" will appear. Note: This works in particular for healing skills that you use on your allies, but the inverse way.
This could inform you about the type(s) of an opponent Minion that you meet for the first time. The game displays effectiveness messages for every attack launched in battle, including the non-damaging ones, according to their type. If the Minion has one type Weak and the other one Resistant, it will be Neutral overall.
(Feel free to add here any tactical subtlety involving this minion that you may know from experience.)