The half-lantern PdII2 complexes trans-(O,C)-[Pd(ppz)(μ-O∩N)]2 (1) and trans-(E,N)-[Pd(ppz)(μ-E∩N)]2 (E∩N is a deprotonated 2-substituted pyridine; E = S (2), Se (3); Hppz = 1-phenylpyrazole) were cocrystallized with 1,4-diiodotetrafluorobenzene (FIB) to give cocrystals 1·(FIB) and (2-3)·2(FIB); the parent complexes and the cocrystals were studied by X-ray crystallography. The crystal structure of trans-(O,C)-1·FIB is assembled mainly by the I···O halogen bonding (XB) to give the [@PdII2]O···I(areneF)I···O[@PdII2] linkage, while trans-(E,N)-(2-3)·2(FIB) are built by the joint action of I···Pd and I···E XBs, thus furnishing the PdII2···I(areneF)I···E[@PdII2] (E = S, Se) cluster. Detailed theoretical (DFT) studies with the application of the QTAIM, ELF, NBO, IGM, SAPT, and HSAB methods revealed several types of attractive noncovalent interactions in the cocrystals, namely, the I···Pd, I···E (E = O, S, Se), I···C, π-π-stacking, and π···F interactions. I···Pd is a rare type of XB involving the metal center as an XB acceptor, the Pd···Pd communication facilitating the I···Pd bonding. The I···Pd and I···E bonds are comparable in strength (the bond interaction energies being between -7 and -13 kcal/mol), but the former is controlled by dispersion forces, while the latter is mostly governed by an electrostatic term.