Diffuse hot gas can be traced effectively by its X-ray absorption and emission .
We present a joint-analysis of these tracers to characterize the spatial and temperature distributions of the Galactic hot gas along the sight-line toward the nearby bright active galactic nucleus Mrk 421 .
We also complement this analysis with far-UV O VI absorption observations .
We find that the observed absorption line strengths of O VII and O VIII are inconsistent with the diffuse background emission line ratio of the same ions , if the gas is assumed to be isothermal in a collisional ionization equilibrium state .
But all these lines as well as the diffuse 3/4-keV broad-band background intensity in the field can be fitted with a plasma with a power law temperature distribution .
We show that this distribution can be derived from a hot gaseous disk model with the gas temperature and density decreasing exponentially with the vertical distance from the Galactic plane .
The joint fit gives the exponential scale heights as \sim 1.0 kpc and 1.6 kpc and the middle plane values as 2.8 \times 10 ^ { 6 } K and 2.4 \times 10 ^ { -3 } { cm ^ { -3 } } for the temperature and density , respectively .
These values are consistent with those inferred from X-ray observations of nearby edge-on galaxies similar to our own .