Co2FeAl (CFA) ultrathin films, of various thicknesses (0.9 nm<tCFA<1.8 nm), have been grown by sputtering on Si substrates, using Ir as a buffer layer. The magnetic properties of the structures have been studied by vibrating sample magnetometry (VSM), miscrostrip ferromagnetic resonance (MS-FMR) and Brillouin light scattering (BLS) in the Damon-Eshbach geometry. VSM characterizations show that films are mostly in-plane magnetized and the perpendicular saturating field increases with decreasing CFA thickness suggesting the existence of interface anisotropy. The presence of magnetic dead layers of 0.44 nm has been detected by VSM. The MS-FMR with perpendicular applied magnetic field has been used to determine the gyromagnetic factor. The BLS measurements reveal a pronounced nonreciprocal spin waves propagation, due to the interfacial Dzyaloshinskii-Moriya interaction (DMI) induced by Ir interface with CFA, which increases with decreasing CFA thickness. The DMI sign has been found to be the same (negative) as that of Pt/Co, in contrast to the ab-initio calculation on Ir/Co. The thickness dependence of the effective DMI constant shows the existence of two regimes similarly to that of the perpendicular anisotropy constant. The DMI constant Ds was estimated to be -0.37 pJ/m for the thickest samples where a linear thickness dependence of the effective DMI constant has been observed.