Rotational spectra of the H-2-HCCCN complex were studied using a pulsed-nozzle Fourier transform microwave spectrometer. Complexes containing the main and several minor isotopologues of cyanoacetylene ((HCCCN)-N-15, DCCCN, and various C-13 containing isotopologues) and the two spin isomers of the H-2 molecule (paraH(2) and orthoH(2)) were investigated. Transitions of complexes with N-14 and D containing isotopologues have nuclear quadrupole hyperfine structures, which were measured and analyzed. Transitions of orthoH(2) molecule containing complexes show additional hyperfine structures due to nuclear magnetic proton spin-proton spin coupling of the hydrogen nuclei in the H-2 molecule. For orthoH(2)-HCCCN, both strong a- and weaker b-type transitions were measured and analyzed using a semirigid asymmetric rotor model. For the paraH(2)-HCCCN complex, only a-type transitions could be observed. The dimer complexes are floppy and have near T-shaped structures. Intermolecular interaction potential energy surfaces were calculated for H-2-HCCCN using the coupled cluster method with single and double excitations and noniterative inclusion of triple excitations [CCSD(T)]. Three orientations of the hydrogen molecule within the complex were considered. Equal weighting of the surfaces corresponding to the three hydrogen orientations provided an averaged potential energy surface. Bound state rotational energy levels supported by the surfaces were determined for the different hydrogen orientations, as well as for the averaged surface. Simple scaling of the surfaces improved the agreement with the experimental results and produced surfaces with near spectroscopic accuracy.