DNA-covered materials are important in technological applications such as biosensors and microarrays, but obtaining structural information on surface-bound biomolecules is experimentally challenging. In this paper, we structurally characterize single-stranded DNA monolayers of poly(thymine) from 10 to 25 bases in length with an emerging surface technique called two-dimensional sum frequency generation (2D SFG) spectroscopy. These experiments are carried out by adding a mid-IR pulse shaper to a femtosecond broad-band SFG spectrometer. Cross peaks and 2D line shapes in the 2D SFG spectra provide information about structure and dynamics. Because the 2D SFG spectra are heterodyne detected, the monolayer spectra can be directly compared to 2D infrared (2D IR) spectra of poly(thymine) in solution, which aids interpretation. We simulate the 2D SFG spectra using DFT calculations and an excitonic Hamiltonian that relates the molecular geometry to the vibrational coupling. Intrabase cross peaks help define the orientation of the bases and interbase cross peaks, created by coupling between bases, and resolves features not observed in ID SFG spectra that constrain the relative geometries of stacked bases. We present a structure for the poly(T) oligomer that is consistent with the 2D SFG data. These experiments provide insight into the DNA monolayer structure and set precedent for studying complex biomolecules on surfaces with 2D SFG spectroscopy.