The present paper extends the hybrid atomistic-continuum multiscale method developed in Vu et al. (2016) to the study of gas flow problems in long microchannels involving density variations. The simulation domain is decomposed into three regions: the bulk where the continuous Navier-Stokes and energy equations are solved, the neighbourhood of the wall simulated by the Molecular Dynamics and the overlap region which connects the macroscopic variables (density, velocity and temperature) between the two former regions. For the simulation of long micro/nano-channels, a strategy with multiple molecular blocks all along the fluid/solid interface is adopted to capture accurately the macroscopic velocity and temperature variations. The validity of the hybrid method is shown by comparisons with a simplified analytical model in the molecular region. Applications to compressible and condensation problems are also presented and the results are discussed. The hybrid method proposed in this paper allows us a cost-effective computer simulations of large scales problems with an accurate modelling of the transfers at small scales (velocity slip, temperature jump, thin condensation films, ...).