We report on atomistic simulations of DPPC lipid monolayers using the CHARMM36 lipid force field and four-point OPC water model. The entire two-phase region where domains of the `liquid-condensed (LC) phase coexist with domains of the `liquid-expanded (LE) phase has been explored. The simulations are long enough that the complete phase-transition stage, with two domains coexisting in the monolayer, is reached in all cases. Also, system sizes used are larger than in previous works. As expected, domains of the minority phase are elongated, emphasizing the importance of anisotropic van der Waals and/or electrostatic dipolar interactions in the monolayer plane. The molecular structure is quantified in terms of distribution functions for the hydrocarbon chains and the PN dipoles. In contrast to previous work, where average distributions are calculated, distributions are here extracted for each of the coexisting phases by first identifying lipid molecules that belong to either LC or LE regions. The three-dimensional distributions show that the average tilt angle of the chains with respect to the normal outward direction is $(39.0pm 0.1)^{circ}$ in the LC phase. % and $(48.1pm 0.5)^{circ}$ in the LC phase. In the case of the PN dipoles the distributions indicate a tilt angle of $(110.8pm 0.5)^{circ}$ in the LC phase and $(112.5pm 0.5)^{circ}$ in the LE phase. These results are quantitatively different from previous works, which indicated a smaller normal component of the PN dipole. Also, the distributions of the monolayer-projected chains and PN dipoles have been calculated. Chain distributions peak along a particular direction in the LC domains, while they are uniform in the LE phase. Long-range ordering associated with the projected PN dipoles is absent in both phases.