By acquiring the FID signal in two-dimensional TD-NMR spectroscopy, it is possible to characterize mixtures or complex samples composed of solid and liquid phases. We have developed a new sequence for this purpose, called IR-FID-CPMG, making it possible to correlate spin-lattice T1 and spin-spin T2 relaxation times, including both liquid and solid phases in samples. We demonstrate here the potential of a new algorithm for the 2D inverse Laplace transformation of IR-FID-CPMG data based on an adapted reconstruction of the maximum entropy method, combining the standard decreasing exponential decay function with an additional term drawn from Abragam’s FID function. The results show that the proposed IR-FID-CPMG sequence and its related inversion model allow accurate characterization and quantification of both solid and liquid phases in multiphasic and compartmentalized systems. Moreover, it permits to distinguish between solid phases having different T1 relaxation times or to highlight cross-relaxation phenomena.