We report on the transport properties of hybrid devices obtained by depositing graphene on a LaAlO3/SrTiO3 oxide junction hosting a 4 nm-deep 2-dimensional electron system. At low graphene-oxide inter-layer bias, the two electron systems are electrically isolated, despite their small spatial separation. A very efficient reciprocal gating of the two neighboring 2-dimensional systems is shown. A pronounced rectifying behavior is observed for larger bias values and ascribed to the interplay between electrostatic field-effects and tunneling across the LaAlO3 barrier. The relevance of these results in the context of strongly coupled bilayer systems is discussed.