Get expressions of E and H fields at a boundary from expression of surface current - Pozar ex 1.11
With a discontinuity the tangential fields are equal, the normal fields are not.

The normal fields are not only if there is a surface charge, if there is a surface charge then use the equations below:




Source: http://www.antenna-theory.com/tutorial/electromagnetics/electric-field-boundary-conditions.php

The only difference is now you are given a surface charge density so to find the magnetic field component, you must take the gradient of the surface charge which will vary by the equation given. 

The difference is you are given a surface charge density