This paper presents a microwave (MW)/millimeter-wave (MMW) triple-band shared-aperture antenna. It is implemented by integrating a differentially-fed patch (3.6 GHz) and a dual-band transmitarray (TA) (26 GHz and 39 GHz) through structure reuse. To realize an efficient integration, the patch antenna is evolved from a single-layer structure to a multi-layer one, with an extended ring-shaped patch added in each layer to obtain a proper transmitting surface (TS) size. For the TA, it adopts a unit cell (UC) consisting of two interleaved slots. By adjusting the lengths of the slots, independent dynamic phase shifts covering 360∘ can be attained for the 26 GHz and 39 GHz bands, respectively. To achieve an appropriate focal-to-diameter ratio (F/D) for the TA, a frequency selective surface (FSS) is employed to replace the ground plane of the patch antenna. Thanks to the spatial feeding architecture of the TA, the proposed antenna eliminates the need of complicated feeding network and features low feeding loss and high gain in the MMW bands. To validate the design idea, a prototype is fabricated and measured. The experimental results demonstrate that the proposed antenna can successfully operate in the three bands with peak gain of 7.6 dBi, 19.3 dBi and 19.5 dBi, respectively. In the 26 GHz and 39 GHz bands, beam scanning ranges of ±25∘ and ±13∘ can be obtained, respectively. The proposed antenna can be a promising candidate for 5G multi-band applications.