We find the existence of two kinds of solitons at the interface of optical superlattices with both spatially modulated nonlinearity and linear refraction index. The first kind of solitons can either drift across the lattice, or deflect to the uniform nonlinear medium. The dynamics of such solitons mainly depends on their powers. The other kind of solitons can stably propagate along the surface, and can be controlled by additional Gaussian beams. In addition, we demonstrate the input-angle-dependent reflection, trapping, and refraction with nearly no losses by launching sech-shaped solitons.