f[x_,y_] := {F@@x, G@@y}

Through[f[g, h][{1,2,3,4,5,6,7,8,9}]]

Through[f[g[#]&, h[#]&][{1,2,3,4,5,6,7,8,9}]]

{g[{1, 2, 3, 4, 5, 6, 7, 8, 9}], h[{1, 2, 3, 4, 5, 6, 7, 8, 9}]}

{F[g[#1]][{1, 2, 3, 4, 5, 6, 7, 8, 9}], G[h[#1]][{1, 2, 3, 4, 5, 6, 7, 8, 9}]}

ReleaseHold[Through[Hold[f][g, h][{1, 2, 3, 4, 5, 6, 7, 8, 9}]]]

{F[{1, 2, 3, 4, 5, 6, 7, 8, 9}], G[{1, 2, 3, 4, 5, 6, 7, 8, 9}]}