The only type of hole that shows up (in red) on a solid object from Properties/Reach is "Normal" ("Through and Next Face do not respond to placement at all).
Unfortunately it does that, even in the latest 2016, the various types of hole will still work ok, i.e. select face, select point, (I use a cross), and click finish, it just doesn't show some of them as a red preview, I don't know any way round it.
A normal hole is blind and has a depth and even on an item thickness of 3mm the hole looks as though it caries on to the depth selected in "Properties".
But even then after deselecting the hole tool (the hole up until now displayed in red) disappears.
A 'normal' hole should work whether its more or less than the thickness of the object, I just wondered if you may have missed clicking 'finish' after setting up the hole.