When a wideband antenna is backed by an artificial magnetic conductor (AMC) reflector, the bandwidth is reduced. With the optimization of the shape of the AMC it is possible to exhibit multiband behavior, but the problem becomes complex if the bands are also intended to be wide. In this study, a methodology that exploits both the expected in-band and out-of-band behaviors of a dual-band AMC was used to design a low-profile, triple-band, and wideband directive antenna. The methodology was validated with a prototype suitable for the European standards of 4G/5G and Wi-Fi 2.4/5/6E, operating within the following bands: 2.4–2.7 GHz, 3.4–3.8 GHz, and 5.17–6.45 GHz. The measured results showed respective peak values of 8.0, 9.1, and 10.5 dBi for the broadside realized gain, front-to-back ratios larger than 19 dB, cross-polarized levels lower than -18 dB, and stable half-power beamwidths within each band. Furthermore, 3 dB gain bandwidths of 34.4%, 19.7%, and 31.0% were also measured.