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The authors deal with mode and parameter-dependent robust mixed H2/Hinfinfiltering design for a class of discrete-time switched polytopic linear systems. The objective is to design a homogeneous switched mixed H2/Hinfin filter guaranteeing the asymptotic stability of the resulting filtering error systems with given performance measures. Based on a switched parameter-dependent Lyapunov function combined with Finsler's lemma, some novel conditions for robust H2 and Hinfin H performance analysis are proposed and in turn the filter synthesis is developed. It is shown that by using a new linearisation technique combined with a bounding approach, the filter gains can be obtained by solving a set of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness and less conservatism of the proposed approach.