Capacitance but Charges are Continuously Spread Out Many textbooks explain that CV = Q, where C is the capacitance of the system, Q is the charge, and V is the voltage difference between terminals. This is commonly used to evaluate C = Q/V, often utilizing the Maxwell equations to calculate V or Q.
However, how should we calculate C when the charges are scattered throughout the system in a continuous manner? 
Below is an example of such a situation, provided solely to help you understand what kind of situations I am talking about:


*

*There are two Iron plates, placed to be parallel with the xy plane, with one place on z=0, the other on z=L. 

*An inhomogeneous & lossy dielectric medium of thickness L is placed between the plates. The permeability of the material $\epsilon$ does not vary with the location, but the conductivity varies with z, perhaps, linearly from $\sigma_1$ at z=0 to $\sigma_2$ at z=L. 

*=>You will see that there are free charges in the dielectric medium as well, spread out in a continuous manner, and you cannot make the iron plates hold Q, -Q charge unless Q=0.

 A: In the physical system described, there’s still a specific voltage V between the (conducting) iron plates. There’s a specific total charge Q. 
Calculating either of those might be hard, but in the physical world they are well defined quantities. 
They then allow the usual C = Q/V calculation. 
Unless the dielectric has a nonlinear response (not just inhomogeneous), this is a linear relationship: double the total charge, the new charge will distribute itself to double the charge density at each point, and the voltage will double. Hence C remains the same well-defined value. 
A: Real capacitors have leakage currents. Your scenario isn't much difference, except we can assume the leakage current is high enough that it interferes with attempts to measure the capacitance by straightforward means.
To a first approximation, your structure will behave like a capacitor and resistor in parallel:

As such, you could determine the effective capacitance by applying an AC voltage, and measuring the AC current produced by the voltage source to deliver that voltage. 
We then have the admittance of the structure at this frequency, and we can determine the capacitance from the imaginary part of the admittance:
$$Y = \frac{\tilde{I}}{\tilde{V}} = \frac{1}{R} + j\omega C$$
$$ C = \frac{\Im\ \{Y\}}{\omega}$$
If we haven't physically build the structure, we could perform a simulation of this measurement using, for example, a finite element method.
We will likely find that the effective capacitance is not the same at different frequencies, and so if we want a model that accounts for the behavior over a wide frequency range we might have to consider a more complicated equivalent circuit, the nature of which might depend on the exact structure being considered. In your example, a series of RC-parallel elements is likely to model the structure effectively, at least up to the frequency where current spreading in the transverse dimensions becomes important:

In this case, extracting the equivalent circuit parameters from measurements or simulations becomes an optimization problem rather than a simple calculation.
