Context. The afterglows and host galaxies of long gamma-ray bursts (GRBs) offer unique opportunities to study star-forming galaxies in the high-z Universe. Until recently, however, the information inferred from GRB follow-up observations was mostly limited to optically bright afterglows, biasing all demographic studies against sight-lines that contain large amounts of dust. Aims. Here we present afterglow and host observations for a sample of bursts that are exemplary of previously missed ones because of high visual extinction (A GRB V 1 mag) along the sight-line. This facilitates an investigation of the properties, geometry, and location of the absorbing dust of these poorly-explored host galaxies, and a comparison to hosts from optically-selected samples. Methods. This work is based on GROND optical/NIR and Swift/XRT X-ray observations of the afterglows, and multi-color imaging for eight GRB hosts. The afterglow and galaxy spectral energy distributions yield detailed insight into physical properties such as the dust and metal content along the GRB sight-line and galaxy-integrated characteristics such as the host's stellar mass, luminosity, color-excess, and star-formation rate. Results. For the eight afterglows considered in this study, we report for the first time the redshift of GRB 081109 (z = 0.9787±0.0005), and the visual extinction towards GRBs 081109 (A GRB V = 3.4 +0.4 −0.3 mag) and 100621A (A GRB V = 3.8 ± 0.2 mag), which are among the largest ever derived for GRB afterglows. Combined with non-extinguished GRBs, there is a strong anti-correlation between the afterglow's metal-to-dust ratio and visual extinction. The hosts of the dustiest afterglows are diverse in their properties, but on average redder ( (R − K) AB ∼ 1.6 mag), more luminous ( L ∼ 0.9 L * ), and massive ( log M * [M ] ∼ 9.8) than the hosts of optically-bright events. Hence, we probe a different galaxy population, suggesting that previous host samples miss most of the massive and metal-rich members. This also indicates that the dust along the sight-line is often related to host properties, and thus probably located in the diffuse ISM or interstellar clouds and not in the immediate GRB environment. Some of the hosts in our sample, are blue, young, or of low stellar mass illustrating that even apparently non-extinguished galaxies possess very dusty sight-lines owing to a patchy dust distribution. Conclusions. The afterglows and host galaxies of the dustiest GRBs provide evidence of a complex dust geometry in star-forming galaxies. In addition, they establish a population of luminous, massive, and correspondingly chemically evolved GRB hosts. This suggests that GRBs trace the global star-formation rate better than studies based on optically selected host samples indicate, and that the previously claimed deficiency of high-mass hosts was at least partially a selection effect.