The photonics-assisted millimeter-wave (MMW) communication technology is attractive to facilitate the MMW application in the upcoming B5G and 6G networks. However, its generated MMW signal by optical heterodyne detection usually suffers from serious laser phase noise, which will severely deteriorate the system performance. In this paper, based on a single dual-drive Mach-Zehnder modulator and a single-end photodetector, we first present a simple and spectrally efficient hybrid fiber-wireless double-sideband transmission by employing an overlapping frequency multiplexing scheme. That is, two independent wireless signals with an identical carrier frequency can be simultaneously transmitted in the hybrid fiber-wireless links. To recover the above two overlapped signals, and cancel the concomitant laser phase noise at the same time, a novel digital signal processing method for carrier extraction and signal recovery is further proposed. A proof-of-concept experiment using two independent 3-GBd quadrature phase shift keying (QPSK) signals at W band (92.5 GHz) is performed. After up to 80-km fiber and 3-m wireless transmission, the two QPSK signals can be successfully demodulated, without using the traditional carrier phase estimation algorithm. The proposed scheme not only can double the spectral efficiency of conventional double sideband transmission scheme, but also is immune to its power fading phenomenon induced by chromatic dispersion and robust to the laser phase noise resulting from two free-running lasers in the photonics-assisted MMW communication link.