An aircraft nose radome has a first portion that is transparent to X band microwave energy, and a second portion that is transparent to W band microwave energy. The second portion may be an insert that is secured to the radome at an opening formed therein. The insert may have a multi-layer structure with first, second and third layers, a fourth layer of foam between the first and second layers, and a fifth layer of foam between the second and third layers. The insert may include a plurality of spaced-apart, elongated reinforcing members or ribs between the first and second layers and between the second and third layers that extend along a longitudinal direction defined by the insert. The insert may have a serrated cross-sectional configuration.