In this article, a novel dual band (DB) filtering power divider (FPD) with full-frequency isolation is presented. The proposed topology consists of 4 coupled line sections (CLSs), 2 ring resonators (RRs), 2 shunted stepped impedance resonators (SIRs), 2 transmission lines (TLs) and 1 isolation network (INW). Through mathematical analysis of its S₁₁ and S₂₁ parameters, simultaneous equations for characteristic impedances are derived with the proposed algorithm. In-band equal-ripple and 6 out-of-band transmission zeros (TZs) can be obtained. In order to realize full-frequency isolation performance, the closed-form design equations and their circuit simulation results of four types of INW are newly summarized and discussed in detail. The isolation level can be adjusted by virtue of the position of the extra TZ of S₃₂ parameter in the desired passband. For verification of the proposed synthesis theory, a general design flowchart is provided, several design examples are then selected and compared in detail. Finally, an DB FPD prototype is designed and fabricated for experimental demonstration. Measured results match the proposed theory very well, and the isolation level is below -20.4 dB in full-frequency range.