The Dresselhaus spin orbit interaction is expected to perturb the quantum spin Hall phase predicted to arise within InAs/GaSb coupled quantum wells. As such, to gain a greater understanding of this spin-orbit interaction, the spin orbit coupling in two InAs/GaSb coupled quantum wells, grown along the [001] axis, is investigated along 3 different in-plane crystallographic axes. Due to the crystallographic axis dependence of the Dresselhaus spin orbit coupling, we can deconvolute this coupling from the axis-invariant Rashba spin orbit coupling. We find that the Dresselhaus parameter is robust against an external gate bias and small changes in growth conditions, with an associated Dresselhaus parameter of (0.20±0.07)10-11 eVm being measured across all samples and top gate bias conditions. In addition we show that the asymmetries associated with the coupled quantum well structure, leading to the Rashba spin orbit coupling, are likely to play a dominant role in determining the spin orbit interaction experienced by a quantum spin Hall state as the system is tuned towards charge neutrality.