Photoexcited intralayer excitons in van der Waals heterostructures (vdWHs) with type-II band alignment have been observed to tunnel into interlayer excitons on ultrafast timescales. Such interlayer excitons have sufficiently long lifetimes that inducing dissociation with external in-plane electric fields becomes an attractive option of improving efficiency of photocurrent devices. In the present paper, we calculate interlayer exciton binding energies, Stark shifts, and dissociation rates for six different transition metal dichalcogenide (TMD) vdWHs using a numerical procedure based on exterior complex scaling (ECS). We utilize an analytical bilayer Keldysh potential describing the interaction between the electron-hole pair, and validate its accuracy by comparing to the full multilayer Poisson equation. Based on this model, we obtain an analytical weak-field expression for the exciton dissociation rate. The heterostructures analysed are MoS2/MoSe2, MoS2/WS2, MoS2/WSe2, MoSe2/WSe2, WS2/MoSe2, and WS2/WSe2 in various dielectric environments. For weak electric fields, we find that WS2/WSe2 supports the fastest dissociation rates among the six structures. We, furthermore, observe that exciton dissociation rates in vdWHs are significantly larger than in their monolayer counterparts.