The detailed distribution and kinematics of the atomic and the CO-bright molecular hydrogen in the disc of the Milky Way inside the solar circle are derived under the assumptions of axisymmetry and pure circular motions. We divide the Galactic disc into a series of rings, and assume that the gas in each ring is described by four parameters: its rotation velocity, velocity dispersion, midplane density and its scale height. We fit these parameters to the Galactic H I and 12CO (J = 1-0) data by producing artificial H I and CO line-profiles and comparing them with the observations. Our approach allows us to fit all parameters to the data simultaneously without assuming a-priori a radial profile for one of the parameters. We present the distribution and kinematics of the H I and H2 in both the approaching (QIV) and the receding (QI) regions of the Galaxy. Our best-fit models reproduces remarkably well the observed H I and CO longitude-velocity diagrams up to a few degrees of distance from the midplane. With the exception of the innermost 2.5 kpc, QI and QIV show very similar kinematics. The rotation curves traced by the H I and H2 follow each other closely, flattening beyond R = 6.5 kpc. Both the H I and the H2 surface densities show a) a deep depression at 0.5 <R <2.5 kpc, analogous to that shown by some nearby barred galaxies, b) local overdensities that can be interpreted in terms of spiral arms or ring-like features in the disc. The H I (H2) properties are fairly constant in the region outside the depression, with typical velocity dispersion of 8.9 ± 1.1 (4.4 ± 1.2) km s-1, density of 0.43 ± 0.11 (0.42 ± 0.22) cm-3 and HWHM scale height of 202 ± 28 (64 ± 12) pc. We also show that the H I opacity in the LAB data can be accounted for by using an "effective" spin temperature of 150 K: assuming an optically thin regime leads to an underestimate of the H I mass by about 30%.