The impedance of a microstrip is calculated with respect to the nearest return path. There is no characteristic impedance with reference to the "hole".
You use the distance to the nearest conducting return path, the width of the strip, the thickness of the strip, and the permetivity of the dielectric(s) to calculate the impedance at any point. The "hole" only serves to increase the distance between the strip and it's reference return conductor. The same equations apply that are used for normal strip impedance calculations.