In this paper, the stability and positive stabilization issues are addressed for discrete-time impulsive switched positive linear systems (DISPLSs) with a novel extended-sequence-pair-dependent (ESPD) hybrid signal. The combination of some common switching and impulsive signals can be seen as special cases of ESPD hybrid signal, such as the arbitrary (dwell time) switching signal and non-periodic (periodic) impulsive signals. Firstly, several necessary and sufficient stability conditions are given for DISPLSs with ESPD hybrid signal. Secondly, based on the non-conservative stability criteria, several necessary and sufficient positive stabilization conditions are presented. Thirdly, the results are extended to the time-delayed cases. Non-conservative stability and stabilization conditions for DISPLSs with multiple time delays are presented. All the results are given in terms of linear programming (LP). Finally, the advantages of the results over the literature are illustrated within four examples.