Recent experiments and simulations have shown that the stability of a moving, planar liquid sheet in the presence of a surrounding gas phase is damped by the gas boundary layer. In this work, we derive the linear stability equations by accounting exactly for the boundary layer in the gas phase while ignoring viscosity in the liquid phase. The proposed model equations are quite general and can be used to investigate the stability of a single interface separating liquid and gas phase as well as those of sinuous and varicose modes of a liquid sheet. We focus on the sinuous mode of a planar liquid sheet and show that the predicted growth rates are significantly lower compared to that predicted by the inviscid theory. The predictions compare well with existing numerical solutions obtained on solving the Orr-Sommerfeld equations as well as experimental results.