Summary form only given. Laser filamentation triggered electric discharges are very promising in view of their numerous applications such as the laser lightning rod, plasma aerodynamic control, high-power closing switches and plasma antennas. However, the development and maturation of these technologies rely on a good knowledge of the plasma parameters. To this purpose, we developed an interferometric diagnostic for electron density. However, as the discharge heats the medium, strong hydrodynamic effects emerge and lead to a non-negligible contribution of bound electrons to the plasma refractive index. We consequently record this index simultaneously at two different wavelengths to discriminate between the free and bound electron contributions, so-called two-color interferometry. The interferometer is built in a standard Mach-Zehnder configuration. We use a 8 ns-full width at half maximum Nd:YAG laser to probe the plasma at both 532 and 1064 nm in a transverse geometry. CCD cameras with a 10 μm pixel size are used to record both interferograms at the same time. Phase recovery from interferograms is done using a 1D continuous wavelet transform algorithm coupled to a cost function routine. Phase unwrapping is done following a noncontinuous path of decreasing reliability. Finally, a Fourier-Hankel Abel inversion algorithm allows recovering electron and neutral radial density profiles. The interferometer is demonstrated on ~40 A sparks triggered by femtosecond filamentation. The limiting phase noise of the interferometer is estimated to be 30 mrad RMS at 532 nm.