The transport properties across perovskite oxides heterointerfaces are analyzed. Epitaxial La(2/3)Ca(1/3)MnO3/SrTiO3 (LCMO/STO) heterostructures with different STO insulating-barrier thicknesses are systematically investigated and their behavior compared with LCMO/metal junctions. Atomic force microscopy (AFM) measurements in current-sensing mode show typical features associated with tunneling conduction. Careful analysis of the I-V curves across LCMO/STO heterointerfaces, using the Simmons model in the intermediate voltage range, clearly shows the existence of an interface-induced enhancement of the tunneling barrier of about 1.6 nm on the LCMO side. These results confirm recent theoretical studies predicting electronic phase segregation and the formation of an orbital-ordered insulating phase at the manganite-insulator interface that is a result of the reduction in the number of charge carriers at the interface.