Multiplicity is a ubiquitous characteristic of massive stars. Multiple systems offer us a unique observational constraint on the formation of high-mass systems. Herschel 36 A is a massive triple system composed of a close binary (Ab1-Ab2) and an outer component (Aa). We measured the orbital motion of the outer component of Herschel 36 A using infrared interferometry with the AMBER and PIONIER instruments of ESO's Very Large Telescope Interferometer. Our immediate aims are to constrain the masses of all components of this system and to determine if the outer orbit is co-planar with the inner one. Reported spectroscopic data for all two components of this system and our interferometric data allow us to derive full orbital solutions for the outer orbit Aa-Ab and the inner orbit Ab1-Ab2. For the first time, we derive the absolute masses of mAa = 22.3 ± 1.7, mAb1 = 20.5 ± 1.5, and mAb2 = 12.5 ± 0.9 M⊙. Despite not being able to resolve the close binary components, we infer the inclination of their orbit by imposing the same parallax as the outer orbit. Inclinations derived from the inner and outer orbits imply a modest difference of about 22° between the orbital planes. We discuss this result and the formation of Herschel 36 A in the context of Core Accretion and Competitive Accretion models, which make different predictions regarding the statistic of the relative orbital inclinations.