Ammonium nitrate in fuel-air bombs
Explosives that use ammonium nitrate and a fuel are mostly referred to as ANFO explosives, you might find more detailled information by using that term.

Most explosives used in military (especially bombs) are based on TNT, mostly in the form of Tritonal, a mixture of TNT and aluminium powder. Generally, only outdated bombs use ANFO explosives (due to their low price and ease-of-use). (See BLU-82, which does indeed use ammonium nitrate)

ANFO explosives are rather used in an industrial context, especially mining.

In the common mixture of ammonium nitrate with nitromethane (ANNM), no oxygen from the air is needed to sustain the explosion:

$\ce{3NH4NO3 + 2CH3NO2 -&gt; 4N2 + 2CO2 + 9H2O}$

Since ANFO explosives carry their oxygen with them by definition (the ammonium nitrate molecule contains 3 oxygen atoms), they do not need oxygen from the surroundings and are therefore not thermobaric or fuel.air weapons.