Seismological constraints obtained from receiver function (RF) analysis provide important information about the crust and mantle structure. Here, we explore the utility of the free-surface multiple of the P-wave (PP) and the corresponding conversions in RF analysis. Using earthquake records, we demonstrate the efficacy of PPs-RFs before illustrating how they become especially useful when limited data is available in typical planetary missions. Using a transdimensional hierarchical Bayesian deconvolution approach, we compute robust P-to-S (Ps)- and PPs-RFs with InSight recordings of five marsquakes. Our Ps-RF results verify the direct Ps converted phases reported by previous RF analyses with increased coherence and reveal other phases including the primary multiple reverberating within the uppermost layer of the Martian crust. Unlike the Ps-RFs, our PPs-RFs lack an arrival at 7.2 s lag time. Whereas Ps-RFs on Mars could be equally well fit by a two- or three-layer crust, synthetic modeling shows that the disappearance of the 7.2 s phase requires a three-layer crust, and is highly sensitive to velocity and thickness of intra-crustal layers. We show that a three-layer crust is also preferred by S-to-P (Sp)-RFs. While the deepest interface of the three-layer crust represents the crust-mantle interface beneath the InSight landing site, the other two interfaces at shallower depths could represent a sharp transition between either fractured and unfractured materials or thick basaltic flows and pre-existing crustal materials. PPs-RFs can provide complementary constraints and maximize the extraction of information about crustal structure in data-constrained circumstances such as planetary missions.