Let $๐ฬ (๐ _{k})(H)^{C}_{A}$ be the category of Doi Hom-Hopf modules, $๐ฬ (๐ _{k})_{A}$ be the category of A-Hom-modules, and F be the forgetful functor from $๐ฬ (๐ _{k})(H)^{C}_{A}$ to $๐ฬ (๐ _{k})_{A}$. The aim of this paper is to give a necessary and suffcient condition for F to be separable. This leads to a generalized notion of integral. Finally, applications of our results are given. In particular, we prove a Maschke type theorem for Doi Hom-Hopf modules.