Various isotopomers of the free dibridged disilyne molecule, Si(H-2)Si, have been observed by millimeter- and submillimeter-wave spectroscopy in a silane-argon plasma produced by an abnormal electric discharge. In order to make measurement of the weak absorption lines possible a novel computer processing treatment has been developed. From the molecular constants measured for Si-28(H-2)Si-28, Si-29(H-2)Si-28, Si-30(H-2)Si-28, and Si-28(D-2)Si-28 an accurate substitution structure has been deduced with r(s)(Si-Si)=2.2154 Angstrom, r(s)(Si-H)=1.6680 Angstrom, and angle(HSiSiH)=104.22 degrees The spectrum analysis and the structure determination have been aided by correlated level ab initio calculations resulting in accurate estimates of the equilibrium geometry and rotational constants, the cubic force field, the quartic and sextic centrifugal distortion constants, and the inversion barrier height of dibridged disilyne. The barrier to inversion of the "butterfly-type" Si(H-2)Si molecule must be relatively high as no splitting due to inversion could be experimentally observed.