Heterostructures of graphene (G) or multilayer graphene (MLG) transferred on the graphene oxide (GO) printed layer are considered in the present study. Hillocks with a height of about 60–100 nm are found at the background GO relief of 10–15 nm. Graphene in these heterostructures completely follows the GO relief. The quasi-suspended layers on the hillocks are observed for MLG, and the distance between MLG and GO is estimated up to 20–40 nm. An increase in the MLG thickness is suggested to increase the distance between MLG and GO. Carrier mobility in G/GO heterostructures is found to equal 300–500 cm2/V s. The formation of quasi-suspended MLG/GO structures leads to an increase in the carrier mobility up to 4500 cm2/V s with an increase in the MLG thickness (3–8 nm). The change in the carrier mobility in MLG as a function of voltage sweep direction is also observed. The effect is supposedly connected with the ability of the quasi-suspended layer to corrugate under the gate voltage application. The capsulation of heterostructures using GO films leads to the carrier mobility degradation to 300–500 cm2/V s in one–four weeks. The quasi-suspended structures are promising for flexible and/or printed electronics at the use as graphene channels for sensors, detectors and other applications.