We present a study of the electronic structure and magnetism of Co$_2$MnAl, CoMnVAl and their heterostructure. We employ a combination of density-functional theory and dynamical mean-field theory (DFT+DMFT). We find that Co$_2$MnAl is a half-metallic ferromagnet, whose electronic and magnetic properties are not drastically changed by strong electronic correlations, static or dynamic. Non-quasiparticle states are shown to appear in the minority spin gap without affecting the spin-polarization at the Fermi level predicted by standard DFT. We find that CoMnVAl is a semiconductor or a semi-metal, depending on the employed computational approach. We then focus on the electronic and magnetic properties of the Co$_2$MnAl/CoMnVAl heterostructure, predicted by previous first principle calculations as a possible candidate for spin-injecting devices. We find that two interfaces, Co-Co/V-Al and Co-Mn/Mn-Al, preserve the half-metallic character, with and without including electronic correlations. We also analyse the magnetic exchange interactions in the bulk and at the interfaces. At the Co-Mn/Mn-Al interface, competing magnetic interactions are likely to favor the formation of a non-collinear magnetic order, which is detrimental for the spin-polarization.
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