A simple cubic lattice model and a matrix formalism are used to calculate the segment density distribution and structural properties of monolayers consisting of end-attached chains and solvent molecules. The chain stiffness, the nearest-neighbor bond correlations, and the intermolecular interactions are taken into account. The calculations are performed for chains of various lengths, from short to polymer brushes. The main difference between the present treatment and those already available consists in the more compact formulation of the basic equations. The incorporation of the nearest-neighbor bond correlations, or higher values of the interaction parameter results in a higher average segment density and a narrower distribution profile of the chain free ends. With decreasing chain length, the effect of the bond correlations becomes less important. The model allows us to calculate the density profiles of the lateral, forward, and backward bonds as a function of the layer number, and to calculate the orientational probability for a bond to be lateral, forward, or backward as a function of the bond number counted from the attached end.