Interdigitated configuration allows two electrode to stick into "each other" and "infuse" together. As a result, the distance between two electrodes can be reduced to a much smaller value than conventional thin film architectures. The reduced distance between electrodes enables fast ion diffusion that results in better rate capability and power density performance.
I used to work with Interdigitated electrodes measuring by EIS. You say for measuring in-plane capacitance, but if you modify the surface, specially between electrodes, it is better to register the resistance. See one of our papers:
Article Impedimetric label-free sensor for specific bacteria endotox...
The benefit of interdigitated electrodes (IDE) in sensor applications is the large gap area between electrodes. The sensing material will occupy this area which will provide large number of binding location between the sensing material and analyte.