Ultraviolet photoelectron spectroscopy is carried out to measure the energy discontinuity at the interface of p-type Na-doped MgZnO (NMZO)/n-type Ga-doped ZnO (GZO) heterojunction grown by dual ion beam sputtering. The offset values at valence band and conduction band of NMZO/GZO heterojunction are calculated to be 1.93 and -2.36 eV, respectively. The p-type conduction in NMZO film has been confirmed by Hall measurement and band structure. Moreover, the effect of Ar+ ion sputtering on the valence band onset values of NMZO and GZO thin films has been investigated. This asymmetric waveguide structure formed by the lower refractive index of GZO than that of NMZO indicates that easy extraction of photons generated in GZO through the NMZO layer into free space. The asymmetric waveguide structure has potential applications to produce ZnO-based light emitters with high extraction efficiency.