In this paper, we construct feedback controllers, explicitly parameterized in a single parameter epsilon, that solve the well-known H-infinity almost disturbance decoupling problem with measurement feedback and with internal stability (H-infinity-ADDPMS) for discrete-time linear systems. In particular, we explicitly construct parameterized solutions for the following three cases: the full state feedback, the full information feedback and the general measurement output feedback. The first two cases have static solutions while the last one has only dynamic solutions. Both the full order and the reduced order measurement feedback controllers are presented for the latter case. The problem considered in this paper is general and complete.