The very exotic nuclear resonance systems, 10He and 13Li, are produced in proton-knockout reactions from relativistic beams of 11Li and 14Be. The experimentally determined energy and angular correlations between their decay products, <img src="http://ars.els-cdn.com/content/image/1-s2.0-S0375947410006044-si1.gif" data-inlimgeid="1-s2.0-S0375947410006044-si1.gif" data-loaded="true" /> and <img src="http://ars.els-cdn.com/content/image/1-s2.0-S0375947410006044-si2.gif" data-inlimgeid="1-s2.0-S0375947410006044-si2.gif" data-loaded="true" />, are analyzed using an expansion of decay amplitudes in a restricted set of hyperspherical harmonics. By considering only a small number of terms it is possible to extract the expansion coefficients directly from the experimental three-body correlations. This provides a model-independent way of getting information about the decay process, on the structure of the decaying nucleus and on the quantum characteristics of the binary subsystems.The results show that the <img src="http://ars.els-cdn.com/content/image/1-s2.0-S0375947410006044-si3.gif" data-inlimgeid="1-s2.0-S0375947410006044-si3.gif" data-loaded="true" /> relative-energy spectrum can be interpreted as consisting of two resonances, an Iπ=0+ ground state and an excited Iπ=2+ state. The <img src="http://ars.els-cdn.com/content/image/1-s2.0-S0375947410006044-si6.gif" data-inlimgeid="1-s2.0-S0375947410006044-si6.gif" data-loaded="true" /> relative-energy spectrum is interpreted as an Iπ=3/2− ground state overlapping with excited states having a structure similar to the 2+ state in 10He but spread over several states due to the coupling to the Iπ=3/2− core. The13Li data also give evidence for a contribution of a configuration where the two neutrons occupy the d-shell.