  We have used the WHAM H_alpha survey and Leiden/Dwingeloo HI data to
decompose the Far-infrared emission (from 100 to 1000 micron) at high Galactic
latitude into components associated with the Warm Ionised Medium (WIM) and the
Warm Neutral Medium (WNM). This decomposition is possible for the first time
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 WIM
(Lagache et al. 1999) and show that the WIM dust temperature and emissivity are
very similar to those in the WNM. The analysis suggests moreover that about 25%
of the far-IR dust emission at high galactic latitude is uncorrelated with the
HI gas. The decomposition again reveals a Cosmic Far-Infrared Background
(CFIRB) which is determined for the first time from 100 to 1000 micron using
two independant gas tracers.
