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This manuscript quantifies the hydrodynamic drag of a spherical droplet translating in unsteady Stokes flow when the droplet has a thin, complex membrane. All forces (e.g., Stokes drag, Basset forces, unsteady memory forces, etc.) have the same functional form as the drag of a clean spherical droplet, as long as one replaces the interior viscosity with an effective (frequency-dependent) one that depends on the viscoelastic moduli of the membrane. The shear elastic moduli of the membrane do not modify the unsteady drag of the droplet – only the dilatational modes matter. We demonstrate how this result can be obtained using simple symmetry/scaling arguments. The results are written for any linearly viscoelastic membrane, but we in particular examine the cases of a purely viscous membrane, purely elastic membrane, one-mode Maxwell membrane, and one-mode Kelvin-Voigt membrane. For the latter two models, we quantify how the membrane relaxation time alters the time-dependent motion of the droplet.