We investigate spin-dependent thermoelectric transport through a system of two coupled quantum dots attached to reservoirs of spin-polarized electrons. Generally, we focus on the strongly correlated regime of transport. To this end, a slave-boson method for finite U is employed. Our main goal is to show that, apart from complex low-temperature physics, such a basic multilevel system provides a possibility to examine various quantum interference effects, with particular emphasis put on the influence of such phenomena on thermoelectric transport. Apart from the influence of interference effects on spin-degenerate charge transport, we show how spin-dependent transport, induced by ferromagnetic leads, can be modified as well. Finally, we also consider the case where the spin-relaxation time in the ferromagnetic leads is relatively long, which leads to the so-called spin thermoelectric effects.