The phase diagrams and magnetic properties of a ferrimagnetic multilayer system consisting periodically of L layers of spin-1/2 A atoms, L layers of spin-1 B atoms, and a disordered interface in between that is characterized by a random arrangement of A and B atoms of A_pB_1-p type and a negative A-B coupling, are investigated by the use of an effective field method within the framework of a single cluster theory. The effects of the disorder in the interface, the bulk and interface anisotropies and different coupling constants on the magnetic properties are examined in details. A number of characteristic features such as the possibility of a compensation point are found.