A plane capacitor cell with variable gap has been designed in order to detect the complex permittivity of low conductive liquids (up to 500 microS/cm) and the impedance of the sample-electrode interface. The novelty of the cell consists of the simultaneous presence of the field uniformity ensured by a guard ring, an adjustable gap between 300 microm and 6.75 mm (the electrode axial motion avoiding any rotation), and the immersion of the capacitor in the sample reservoir. The size of the capacitor electrodes and the gap values have been tested via the capacitance detection of the in-air cell at 1 kHz. The sample measurements have been performed by scanning the frequency range between 15 Hz and 2 MHz at four different capacitor gap values. In the paper a method to directly extract the bulk complex permittivity and the interface impedance versus frequency is presented. It is based on the assumption that the interface contribution is independent of the electrode gap, as confirmed (within the measurement accuracy) from measurements on all samples investigated. As samples of interest, we have chosen two certified electrolytic conductivity standards, KCl aqueous solutions having conductivity traceable to SI units; and two polymer latex aqueous dispersions of microspheres. Regarding KCl solutions, the conductivity measurements are compatible with the reference values within the specified uncertainty; the measured permittivities are consistent with the literature. For all samples, we have recovered the expected result that the interface impedance mainly affects the low frequency range (f<10 kHz).