We present synthetic Hi and CO observations of a numerical simulation of decaying turbulence in the thermally bistable neutral medium. We first present the simulation, which produces a clumpy medium, with clouds initially consisting of clustered clumps. Self-gravity causes these clump clusters to merge and form more homogeneous dense clouds. We apply a simple radiative transfer algorithm, throwing rays in many directions from each cell, and defining every cell with A v > 1 as molecular. We then produce maps of Hi, CO-free molecular gas, and CO, and investigate the following aspects: i) The spatial distribution of the warm, cold, and molecular gas, finding the well-known layered structure, with molecular gas being surrounded by cold Hi and this in turn being surrounded by warm Hi. ii) The velocity of the various components, finding that the atomic gas is generally flowing towards the molecular gas, and that this motion is reflected in the frequently observed bimodal shape of the Hi profiles. This conclusion is, however, tentative, because we do not include feedback that may produce Hi gas receding from molecular regions. iii) The production of Hi self-absorption (HISA) profiles, and the correlation of HISA with molecular gas. In particular, we test the suggestion of using the second derivative of the brightness temperature Hi profile to trace HISA and molecular gas, finding significant limitations. On a scale of several parsecs, some agreement is obtained between this technique and actual HISA, as well as a correlation between HISA and the molecular gas column density. This correlation, however, quickly deteriorates towards sub-parsec scales. iv) The column density PDFs of the actual Hi gas and those recovered from the Hi line profiles, finding that the latter have a cutoff at column densities where the gas becomes optically thick, thus missing the contribution from the HISA-producing gas. We also find that the powerlaw tail typical of gravitational contraction is only observed in the molecular gas, and that, before the power-law tail develops in the total gas density PDF, no CO is yet present, reinforcing the notion that gravitational contraction is needed to produce this component.