We report a photonic radio frequency (RF) self-interference cancellation (SIC) and harmonic down-conversion (HDC) scheme based on a dual-parallel dual-drive Mach-Zehnder modulator (DDMZM). The proposed scheme can eliminate the chromatic-dispersion induced power fading (CDIP) effect and thus is very suitable for in-band full-duplex (IBFD) radio-over-fiber (ROF) system. The self-interference RF signal is directly cancelled in optical domain, which overcomes the electronics bottleneck limitation of electrical SIC. Moreover, the HDC allows us to use a cost-effective low frequency local oscillation (LO) source to down-convert a high-frequency RF signal into an intermediate frequency (IF) band. In addition, the harmonic odd-order single-sideband (SSB) down-conversion is naturally free from the CDIP effect. The proposed photonic SIC+HDC system is theoretically analyzed and experimentally verified.