Circularly polarized light can rectify orbital motion into a static magnetization through the inverse Faraday effect (IFE), but in electron-hole bilayers the electron and hole contributions cancel exactly when their properties are equivalent. We show that electron-hole bilayers in transition-metal dichalcogenide platforms avoid this cancellation through effective-mass asymmetry alone, and that the surviving orbital IFE is sensitive to interlayer coupling. In the weak-coupling regime, a two-component Drude description yields an induced magnetization of order one Bohr magneton per carrier for representative terahertz driving. In the strong-coupling regime, where the carriers bind into interlayer excitons, we treat the relative motion using a hydrogenic model with a Rytova-Keldysh interaction and obtain a reduced but finite response. We give closed-form expressions that allow estimates across a broad parameter range and identify where the response is largest.