  In the current Dark Energy Spectroscopic Instrument (DESI) survey, emission
line galaxies (ELGs) and luminous red galaxies (LRGs) are essential for mapping
the dark matter distribution at $z \sim 1$. We measure the auto and cross
correlation functions of ELGs and LRGs at $0.8<z\leq 1.0$ from the DESI
One-Percent survey. Following Gao et al. (2022), we construct the galaxy-halo
connections for ELGs and LRGs simultaneously. With the stellar-halo mass
relation (SHMR) for the whole galaxy population (i.e. normal galaxies), LRGs
can be selected directly by stellar mass, while ELGs can also be selected
randomly based on the observed number density of each stellar mass, once the
probability $P_{\mathrm{sat}}$ of a satellite galaxy becoming an ELG is
determined. We demonstrate that the observed small scale clustering prefers a
halo mass-dependent $P_{\mathrm{sat}}$ model rather than a constant. With this
model, we can well reproduce the auto correlations of LRGs and the cross
correlations between LRGs and ELGs at $r_{\mathrm{p}}>0.1$
$\mathrm{Mpc}\,h^{-1}$. We can also reproduce the auto correlations of ELGs at
$r_{\mathrm{p}}>0.3$ $\mathrm{Mpc}\,h^{-1}$ ($s>1$ $\mathrm{Mpc}\,h^{-1}$) in
real (redshift) space. Although our model has only seven parameters, we show
that it can be extended to higher redshifts and reproduces the observed auto
correlations of ELGs in the whole range of $0.8<z<1.6$, which enables us to
generate a lightcone ELG mock for DESI. With the above model, we further derive
halo occupation distributions (HODs) for ELGs which can be used to produce ELG
mocks in coarse simulations without resolving subhalos.
