Looks like you already know about the principle of Mixed function spaces. Make sure you’ve checked against examples at https://bitbucket.org/fenics-project/dolfin/src/master/python/demo/documented/
e.g. https://bitbucket.org/fenics-project/dolfin/src/master/python/demo/documented/mixed-poisson/demo_mixed-poisson.py.rst
I guess you might handle your inner boundary condition with a lagrange multiplier.
Dokken gives more references (published papers) to Cécile Daversin-Catty’s work on mixed spaces at Prescribe discontinuity on internal boundary and also mentions Nitsche’s method as another approach (for discontinuous systems).