The interface condition provides flexibility to handle complex geometries on a set of structured grids. However, when used with a compact scheme to apply in computational aeroacoustics, its accuracy and stability may be degraded seriously by the boundary treatment that arises at a grid interface. To minimize this effect, a modified characteristic condition is incorporated in the finite difference compact scheme by using an explicit difference form at the boundary. The extension of this approach is naturally attained through the coordinate transformation of convective terms across an interface in multidimensions. The validity of current development is demonstrated through a simulation of trailing-edge noise generation from an airfoil at a low Mach number.