Composite radome wall structures (10) exhibit both antiballistic and radar transparency properties and include an antiballistic internal solid, void-free core (12) and external antireflective (AR) surface layers (14-1, 14-2) which sandwich the core. The antiballistic core can be a compressed stack of angularly biased unidirectional polyethylene monolayers formed of tapes and/or fibers. Face sheets (16-1, 16-2) and/or one or more impedance matching layers (27, 28) may optionally be positioned between the antiballistic core and one (or both) of the external AR layers so as to bond the core to the AR surface layer(s) and/or selectively tune the radome wall structure to the frequency of transmission and reception associated with the radar system.