How can I solve a pdepe problem with boundary value problem?

Hi!

I'm trying to solve a problem where 3 components (i) diffuse between 2 regions (j) taking into account spatial and time derivatives.

The equation that represents the difussion is:

Using pdepe solver this problem is easily solved when there is not a boundary between the regions. However, I have the following equilibrium and continuity equations in the interface between the two regions:

I have found that this kind of boundary value problems can be solved with solver bvp5c or solvers that admit a third element Region. I think pdepe does not admit a third element in the BC function

My question is:

Is there any solver that solves spatial and time partial derivative equations with boundary value problems?

Thanks in advance

Marta