We are interested in the approximation of a cardiac microscopic model. It is a set of Laplace equations with non-standard, timedependent, transmission conditions, for which finite volume methods are of real interest. The transmission conditions state as ordinary differential equations on the jump of the potential, namely the transmembrane voltage, so that we keep this voltage as an unknown in our scheme. Here we extend the two-point flux approximation to the discretization of this model, show that it converges, and compute error estimates.