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 (12) 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 may optionally be positioned between the antiballistic core (12) and one (or both) of the external AR layers (14-1, 14-2) 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.