It is a little vague. Infantry are defined on page 7, flyers on page 68-9.
Contrary to what I said above, it would appear that they are not mutulaay exclusive (should have read things properly in the first place).
Infantry are a unit type, together with cavalry, war machines, chariots, characters and monsters.
Flyers are a subclass of the above, and "...follow all the rules for normal units, except for the differences described below." I would therefore say that, taking these together, flyers fall into one of the troop types above, and only infantry can enter buildings. Characters are either monsters or infantry, unless following a special rule of some sort (a centaur would be cavalry, for example).
Therefore all flyers can enter a building, subject to usual restrictions (one unit, with max US of 30 - therefore 30 fell bats :question

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