The fully developed buoyancy-induced (natural convective) Couette-Poiseuille flow in a vertical microchannel is investigated with the velocity slip and temperature jump boundary conditions. Closed form analytical solutions for the velocity and temperature fields are obtained. The effects of the fluid-wall interaction parameter, wall-ambient temperature difference ratio, Knudsen number, mixed convection parameter, and the dimensionless pressure gradient on the velocity, temperature, volume flow rate, heat flux between the plates and the Nusselt number have been discussed in detail through graphs. The outcomes of the investigation indicate that the volume flow rate increases with increasing values of mixed convection parameter, wall-ambient temperature difference ratio, and Knudsen number. © 2017 Published under licence by IOP Publishing Ltd.