We present Infrared Spectrograph spectra and revised Multiband Imaging Photometer photometry for the 18 members of the eta Chamaeleontis cluster. Aged 8 Myr, the eta Cha cluster is one of the few nearby regions within the 5-10 Myr age range, during which the disk fraction decreases dramatically and giant planet formation must come to an end. For the 15 low-mass members, we measure a disk fraction similar to 50%, high for their 8 Myr age, and four of the eight disks lack near-IR excesses, consistent with the empirical definition of "transition" disks. Most of the disks are comparable to geometrically flat disks. The comparison with regions of different ages suggests that at least some of the "transition" disks may represent the normal type of disk around low-mass stars. Therefore, their flattened structure and inner holes may be related to other factors ( initial masses of the disk and the star, environment, binarity), rather than to pure time evolution. We analyze the silicate dust in the disk atmosphere, finding moderate crystalline fractions (similar to 10%-30%) and typical grain sizes similar to 1-3 mu m, without any characteristic trend in the composition. These results are common to other regions of different ages, suggesting that the initial grain processing occurs very early in the disk lifetime (< 1 Myr). Large grain sizes in the disk atmosphere cannot be used as a proxy for age, but are likely related to higher disk turbulence. The dust mineralogy varies between the 8-12 mu m and the 20-30 mu m features, suggesting high temperature dust processing and little radial mixing. Finally, the analysis of IR and optical data on the B9 star eta Cha reveals that it is probably surrounded by a young debris disk with a large inner hole, instead of being a classical Be star.