An atomistic modeling approach is presented for simulating the interface between a polymer melt and a crystalline solid substrate. As a test case, a thin film of polyethylene (PE) melt confined between a semiinfinite graphite phase on the one side and vacuum on the other is considered. The simulation is carried out in the NPT statistical ensemble with an efficient Monte Carlo (MC) algorithm based on state-of-the-art variable connectivity moves. The atomistic simulations are conducted by describing the PE chains with a united atom model, which considers each methylene (CH2) and methyl (CH3) group along the chain backbone as single interaction sites. To calculate the potential energy of interaction between polymer atoms and the semiinfinite graphite substrate, the method designed by Steele was implemented, capable of incorporating the exact crystallographic structure of graphite. The new approach has allowed us to analyze structural and conformational properties on the length scale of just a few angstroms from both surfaces. Detailed results are presented for the local mass density, structure, and conformation of PE at the two interfaces, obtained from simulations with model, strictly monodisperse PE samples of molecular length up to C-400. Additional structural features of the adsorbed layer, such as the distribution of skeletal carbon atoms in train, loop, and tail conformations and their statistics, are also analyzed in detail and compared with the predictions of the lattice-based Scheutjens-Fleer self-consistent meanfield theory in the limit of zero solvent concentration (melt case). Our atomistic simulation data demonstrate a stronger dependence of these descriptors of adsorbed layer structure on chain length than what is calculated by the mesoscopic Scheutjens-Fleer lattice model. In a second step, thoroughly equilibrated configurations of the confined model PE melt films are subjected to detailed molecular dynamics (MD) simulations in the NPT ensemble to analyze their dynamic behavior. The MD simulations are carried out with the rRESPA multiple-time-step algorithm and have allowed us to monitor segmental and chain center-of-mass mean-square displacements over time scales on the order of a few hundreds of nanoseconds. Results from the MD simulations are presented in the companion paper.