Electronic properties of polarity-discontinued heterointerfaces between two perovskite band insulators, LaAlO3 and SrTiO3, have been investigated. Various heterointerfaces with AlO2-LaO/TiO2-SrO and LaO-AlO2/SrO-TiO2 termination including the mixtures of these two domains are fabricated in a single experimental run. This is accomplished by pulsed laser depositions of prescribed coverage (theta(SrO)) of SrO atomic layer on TiO2-terminated SrTiO3 (001) surface and successive LaAlO3 layer, where the processes are regulated in an atomic scale by in situ reflection high-energy electron diffraction. Increasing theta(SrO) from 0 to 1, extra electrons density at the heterointerfaces decreases from a value, close to 0.5 electrons at one Ti site, to zero, while low temperature mobility remains above 100 cm(2)/V(.)s. Our result implies a way to control carrier density in polarity-discontinued heterointerfaces.