FfH uses 2 types of Invisible: INVISIBLE_LAND (super Invis. Shadows use this), and INVISIBLE_ANIMAL (nuisance Invis. Giant Spiders use this)
Most recon units can see INVISIBLE_ANIMAL (pedia will say "Can see Invisible Animals"), Hawks and a few Upper end Recon Units can see INVISIBLE_LAND (pedia will say "Can see Stealth"). Though it is possible to see multiple types of Invis, no units in FfH do so. Thus to have a "single unit" detect everything, you need a hunter carrying a Hawk.
When a Hawk does a Recon Mission, it "personally" views each of the tiles. Thus it will show you all INVISIBLE_LAND units, but none of the INVISIBLE_ANIMAL units, because the Hawk itself cannot see them.
No unit is ever considered Invisible while it is inside a City belonging to the same owner. This means that while a Giant Spider won't defend a Mine against a Warrior (Warrior cannot see it, so won't have any reason to be unable to enter the tile), it can defend a City.
Nox Noctis and Dies Diei are special cases. Nox Noctis makes units Invisible AND Undetectable. Absolutely nothing can EVER reveal them, and no units have even a CHANCE to detect them. Dies Diei will reveal ALL types of Invisible Units, even if you mod in a new Invisible Type of your own and don't provide the ability to see it to any units.
If you own both Dies Diei and Nox Noctis, there is no Conflict. Dies Diei only reveals units that do not belong to you. So while all of your units will be invisible (unless in a city), all other units will be completely visible.
@Frogman: You are using my manual? I just checked and the Elohim & Bannor Worldspells are listed properly.