BTW, what are the figures? Dragon 1/35? If they are, the artwork is likely to be Ron Volstad, a very competent painter (and modeller too, from Canada) who strives for accuracy.
The jump smock was worn over regular luftwaffe uniforms but was retained in combat.
By 1944 the paras ware no longer doing combat jumps and were used mostly as specialised infanty. By the late war supplies were thin on the ground and the jump smock, be it green or camo was considered an item of an elite unit, and as such much prized but the soldiers. They did survive until the late ware but in fewer numbers. You can paint the figure in a green jump smock.