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An investigation of the triplet 3d-complex of $H2$, the $g(3d)3\Sigma g+,1(3d)3\Sigma g$ and) $(3d)3\Delta g$ and the nearby $h(3s)3\Sigma g+$ state, has been performed visible emission spectra have been obtained with a low pressure discharge lamp and recorded by Fourier Transform Spectrometer. Transition wavenumbers and rotational energy levels are given for $v=0-3$ of the four states. The data are represented by an effective Hamiltonian which accounts for the rotational breakdown of the Born-Oppenheimer approximation (L-uncoupling) The eigenvectors obtained from this model provide considerable insight into the nature of the 3d-complex. It has been found necessary to include interactions with the $h(3s)3\Sigma g\mathrm{<mrow\; data-mjx-texclass="ORD">+</mrow>}$ state to describe the complex for lower v values. Molecular constants are also given. Also for M Larzilliere: Laboratoire de Spectrometrie lonique et Moleculaire Associe au CNRS, Universite lyon-1, 69622 Villeurbanne Cedex, FRANCE