We present instrumental (F606W, F814W) and calibrated (V, I) photometry and astrometry for point-like sources in the Hubble Deep Field and its flanking fields from combined HST and Keck direct imaging. From this data, a complete sample of stars in the range 18≤V∼25 is derived and compared to the predictions of a galactic structure model. These comparisons allow to put constraints on the faint end of the disc's luminosity function (LF) as well as on the disc's scale-height. We find that a good representation for the faint disc's LF is provided by Stobie et al. (1989MNRAS.238..709S
) for Mv
>+12, with a slope d logφ(Mv
~-0.3, quite different from the almost flat LF by Wielen et al. (1983IAUCo..76..163W
) derived from the catalogue of nearby stars. This result confirms similar findings from other larger, but less homogeneous, HST samples. The observed red counts (V-I≥3) are best matched by a disc with a scale-height of 250pc, rather than the ``standard'' value of 325pc, in agreement with the determination of this parameter by Kroupa (1992IAUCo.135..228K
) who uses a model that fully includes the effects of stellar binarity in the analysis of photometric parallaxes. We explore the parameter space provided by the galactic model in order to find the best match to the observed starcounts and color counts. It is found that the best match advocates for a round ``external'' (Heliocentric distances of 8 to 10kpc) halo, in agreement with recent findings from the kinematics of blue Horizontal-Branch stars (Wilhelm et al., 1996, ASP Conf. Ser. 92, 171). We find an equally good match between model and observations for a thick-disc with a local (``standard'') normalization of 2% and a scale-height of 1300pc (Reid & Majewski, 1993ApJ...409..635R
), or a local normalization of 6% and a smaller scale height of 750pc (Ojha et al., 1996A&A...311..456O
). The ambiguity of the pair local-normalization to scale-height can not be resolved with star- and color-counts alone and other observational parameters are needed, as demonstrated by Robin et al. (1996) who favor the latter solution.