Want to solve Laplace equation for two mediums separated by an interface

I want to solve the Laplace equation for electrostatics in two different regions separated by an interface. I can’t understand how to impose a continuity condition for the electric field on the interface. Can anyone help me to figure out the problem?

Is there an official supplement on mediums or is it just an AU?

I'm a big fan of mediums (character option, monsters, tradition … everything), and I want to use them in my D & D campaign.

Is there an official supplement to them or is it just an AU?