Context. Planet(s) in binaries are unique architectures for testing predictions of planetary formation and evolution theories in very hostile environments. Their presence in such a highly perturbed region poses a clear challenge from the early phase of planetesimals accretion to the dynamical evolution and stability through a very long period of time (several Gyrs in some case). Aims. The combination of radial velocity, speckle interferometry, high-contrast imaging and high-precision astrometry with interfer-ometry, offers a unique and unprecedented set of observable to push the exploration of the extreme planetary system HD 196885. By dissecting the physical and orbital properties of each component, we aim at shedding light on its global architecture and stability. Methods. We used the IRDIS dual-band imager of SPHERE at VLT, and the speckle interferometric camera HRCAM of SOAR, to acquire high-angular resolution images of HD 196885 AB between 2015 and 2020. Radial velocity observations started in 1983 with CORAVEL at OHP have been extended with a continuous monitoring with CORALIE at La Silla, and ELODIE and SOPHIE at OHP over almost 40 yr extending the radial velocity measurements HD 196885 A and resolving both the binary companion and the inner giant planet HD 196885 Ab. Finally, we took advantage of the exquisite astrometric precision of the dual-field mode of VLTI/GRAVITY (down to 30 µas) to monitor the relative position of HD 196885 A and B to search for the 3.6 yr astrometric wobble of the circumpri-mary planet Ab imprinted on the binary separation. Results. Our observations enable to accurately constrain the orbital properties of the binary HD 196885 AB, seen on an inclined and retrograde orbit (iAB = 120.43 deg) with a semi-major axis of 19.78 au, and an eccentricity of 0.417. The GRAVITY measurements confirm for the first time the nature of the inner planet HD 196885 Ab by rejecting all families of pole-on solutions in the stellar or brown dwarf masses. The most favored island of solutions is associated with a Jupiter-like planet (MAb = 3.39 MJup), with moderate eccentricity (eAaAb = 0.44), and inclination close to 143.04 deg. This results points toward a significant mutual inclination (Ф = 24.36 deg) between the orbital planes (relative to the star) of the binary companion B and the planet Ab. Our dynamical simulations indicate that the system is dynamically stable over time. Eccentricity and mutual inclination variations could be expected for moderate von Zipele Kozai Lidov cycles that may affect the inner planet.