Holes confined in single InAs quantum dots have recently emerged as a promising system for the storage or manipulation of quantum information. These holes are often assumed to have only heavy-hole character and further assumed to have no mixing between orthogonal heavy hole spin projections (in the absence of a transverse magnetic field). The same assumption has been applied to InAs quantum dot molecules formed by two stacked InAs quantum dots that are coupled by coherent tunneling of the hole between the two dots. We present experimental evidence of the existence of a hole spin mixing term obtained with magneto-photoluminescence spectroscopy on such InAs quantum dot molecules. We use a Luttinger spinor model to explain the physical origin of this hole spin mixing term: misalignment of the dots along the stacking direction breaks the angular symmetry and allows mixing through the light-hole component of the spinor. We discuss how this novel spin mixing mechanism may offer new spin manipulation opportunities that are unique to holes. Comment: 13 pages, 9 figures