We have used the WHAM H-alpha survey and Leiden/Dwingeloo HI data to decomp
ose the Far-infrared emission (from 100 to 1000 mu m) at high Galactic lati
tude into components associated with the Warm Ionised Medium (WIM) and the
Warm Neutral Medium (WNM). This decomposition is possible for the first tim
e thanks to preliminary WHAM data that cover a significant fraction of the
sky (about 10%). We confirm the first detection of dust emission from the W
IM (Lagache et al. 1999) and show that the WIM dust temperature and emissiv
ity are very similar to those in the WNM. The analysis suggests moreover th
at about 25% of the far-IR dust emission at high Galactic latitude is uncor
related with the HI gas. The decomposition again reveals a Cosmic Far-Infra
red Background (CFIRB) which is determined for the first time from 100 to 1
000 mu m using two independent gas tracers.