Based on our continuum hydrodynamic model for immiscible two-phase flows at solid surfaces, the stick-slip motion has been predicted for moving contact line at chemically patterned surfaces [Wang et al., J. Fluid Mech., 605 (2008), pp. 59-78]. In this paper we show that the continuum predictions can be quantitatively verified by molecular dynamics (MD) simulations. Our MD simulations are carried out for two immiscible Lennard-Jones fluids confined by two planar solid walls in Poiseuille flow geometry. In particular, one solid surface is chemically patterned with alternating stripes. For comparison, the continuum model is numerically solved using material parameters directly measured in MD simulations. From oscillatory fluid-fluid interface to intermittent stick-slip motion of moving contact line, we have quantitative agreement between the continuum and MD results. This agreement is attributed to the accurate description down to molecular scale by the generalized Navier boundary condition in our continuum model. Numerical results are also presented for the relaxational dynamics of fluid-fluid interface, in agreement with a theoretical analysis based on the Onsager principle of minimum energy dissipation.