Aluminum nitride (AlN) is an emerging material for integrated quantum photonics due to its large χ(2) nonlinearity. Here we demonstrate the hybrid integration of AlN on silicon nitride (SiN) photonic chips. Composite microrings are fabricated by reactive DC sputtering of c-axis oriented AlN on top of pre-patterned SiN. This new approach does not require any patterning of AlN and depends only on reliable SiN nanofabrication. This simplifies the nanofabrication process drastically. Optical characteristics, such as the quality factor, propagation losses and group index, are obtained. Our hybrid resonators can have a one order of magnitude increase in quality factor after the AlN integration, with propagation losses down to 0.7 dB/cm. Using finite-element simulations, phase matching in these waveguides is explored.