Infrared (IR) remote sensing offers a huge range of applications, mostly addressing make-or-break issues of our century (crops water content monitoring, forest fires and volcanic eruption detection and imaging, etc.). These applications fall under different spectral bands, known as mid and long-wave infrared, which are very hard to combine in a single compact instrument. In this article we propose to explore the infrared (IR) behaviour of a dual-band diffractive component: the multilayer diffractive optical element (MLDOE). We use and discuss the thin element approximation as a valid phase model. Using Fourier optics, we are able to simulate the resulting image of the MLDOE. Thereby, ray-tracing software are not accurate to model a complex diffractive component. The Strehl ratio is used to determine the focalization efficiency for the working order, which is above 95% in the mid and long-wave infrared bands. This result, along with the very low energy content of the other orders, proves the strong imaging potential of MLDOEs for dual-band applications. It is also demonstrated that the MLDOE has the same chromatic behaviour as standard DOEs, making it a very useful component for infrared achromatization.