  Determination of the cosmic infrared background (CIB) at far infrared
wavelengths using COBE/DIRBE data is limited by the accuracy to which
foreground interplanetary and Galactic dust emission can be modeled and
subtracted. Previous determinations of the far infrared CIB (e.g., Hauser et
al. 1998) were based on the detection of residual isotropic emission in skymaps
from which the emission from interplanetary dust and the neutral interstellar
medium were removed. In this paper we use the Wisconsin H-alpha Mapper (WHAM)
Northern Sky Survey as a tracer of the ionized medium to examine the effect of
this foreground component on determination of the CIB. We decompose the DIRBE
far infrared data for five high Galactic latitude regions into H I and H-alpha
correlated components and a residual component. We find the H-alpha correlated
component to be consistent with zero for each region, and we find that addition
of an H-alpha correlated component in modeling the foreground emission has
negligible effect on derived CIB results. Our CIB detections and 2 sigma upper
limits are essentially the same as those derived by Hauser et al. and are given
by nu I_nu (nW m-2 sr-1) < 75, < 32, 25 +- 8, and 13 +- 3 at 60, 100, 140, and
240 microns, respectively. Our residuals have not been subjected to a detailed
anisotropy test, so our CIB results do not supersede those of Hauser et al. We
derive upper limits on the 100 micron emissivity of the ionized medium that are
typically about 40% of the 100 micron emissivity of the neutral atomic medium.
This low value may be caused in part by a lower dust-to-gas mass ratio in the
ionized medium than in the neutral medium, and in part by a shortcoming of
using H-alpha intensity as a tracer of far infrared emission.
