Continuum SED models of gamma-ray burst ( GRB ) and obscured GRB host galaxies at moderately high redshifts are presented and compared with those of superluminous supernovae ( SLSN ) , starburst ( SB ) and active galactic nuclei ( AGN ) . We consider that continuum radiation ( bremsstrahlung ) is emitted from the same clouds which emit the line spectrum in each object . Therefore , we have selected from the samples of the GRB host continuum observations those that were previously modelled on the basis of the line spectra , because modelling the continuum SED is less constraining . The bremsstrahlung is generally recognised in the radio and in the UV-X-ray frequency ranges , while dust reradiation peaks in the IR . We have found that GRB980703 host extended clouds have dust-to-gas ratio d / g =0.03 , while for GRB980425 d / g < 0.0001 . To reproduce the continuum SED of most of the GRB , SLSN , SB and AGN in the near-IR-optical range , the contribution of an old star background population is needed . This radiation can be reproduced by a black body ( bb ) corresponding to temperatures T _ { bb } \sim 3000-8000 K. The best fit of a few host SEDs includes also the direct contribution of the bb flux from the SB corresponding to T _ { * } \sim 5 \times 10 ^ { 4 } K . d / g calculated by modelling the SEDs of obscured GRB hosts roughly increases with z resembling the SFR trend .