We proposed a method to simultaneously implement birefringence-phase-matching (BPM) and quasi-phase-matching (QPM) second harmonic generation (SHG) and polarization coupling including six mismatches of wave vectors, in general case, in an optical superlattice (OSL). And the numerical simulations of SHG and polarization coupling in the OSL are carried out. The results indicate that unlike those of SHG processes with only one second harmonic (SH) reported, when one e-polarized fundamental pump is injected into the OSL, another o-polarized fundamental wave, an o-polarized and an e-polarized SHs can be simultaneously generated. The magnitudes of the o-polarized fundamental wave and SHs can be manipulated by an external dc electric field, which is useful when frequency conversion and signal tuning are required simultaneously.