Context. The closest ever fly-by of the Martian moon Phobos, performed by the European Space Agency's Mars Express spacecraft, gives a unique opportunity to sharpen and test the Planetary Radio Interferometry and Doppler Experiments (PRIDE) technique in the interest of studying planet-satellite systems. Aims. The aim of this work is to demonstrate a technique of providing high precision positional and Doppler measurements of planetary spacecraft using the Mars Express spacecraft. The technique will be used in the framework of Planetary Radio Interferometry and Doppler Experiments in various planetary missions, in particular in fly-by mode. Methods. We advanced a novel approach to spacecraft data processing using the techniques of Doppler and phase-referenced very long baseline interferometry spacecraft tracking. Results. We achieved, on average, mHz precision (30 μm/s at a 10 s integration time) for radial three-way Doppler estimates and sub-nanoradian precision for lateral position measurements, which in a linear measure (at a distance of 1.4 AU) corresponds to ∼50 m.