Abstract: We obtain an analytic expression for the response function of a superconductor to an external vector potential in the London limit. We work within the framework of a two-band model with both intra- and interband pairings leading to superconducting (SC) and spin-density wave (SDW) orders, and assume that the mean-field approach is valid. For definiteness, we assume a homogeneous s+- SC order parameter, and a commensurate SDW order parameter. We numerically solve the relevant coupled self-consistency conditions in the zero-temperature limit for the two order parameters, and use those solutions to calculate the London penetration depth dependence on doping, modeled by a doping-dependent anisotropic band-splitting. This would serve as a preliminary guide into future investigation of possible features in the temperature dependence of the London penetration depth, found in recent experiments.