There is a rich history of studying coherent structures in the atmospheric boundary layer through the use of spatial correlations between wall shear stress and elevated velocity measurements. This work has primarily focused on neutral and convective boundary layers, while structures in the stable boundary layer (SBL) have received less attention. We use direct numerical simulations (DNSs) of turbulent channel flow across a range of static stabilities to examine the inclination angles of turbulent structures in the SBL. Angles are inferred not only from wall shear stress and velocity correlations, but also from correlations between the wall buoyancy flux and buoyancy. Results indicate that structures in the SBL have a smaller angle than those under neutral conditions, and that the difference is enhanced with increasing stratification. Specifically, stratification across the range of considered simulations decreases the angles from the neutral case by <1˚ near the surface and by ~1–3˚ at the top of the logarithmic region. Additionally, the angles of buoyancy structures are larger than those inferred from momentum by ~3˚ throughout the entire depth of this layer. Further, angles increase with height until leveling off near the top of the logarithmic region, which may be the result of local $z$-less stratification based on analysis of the Richardson number and normalized standard deviations. The DNS data are in good agreement with both existing published data and newly reported observations from the AHATS field campaign. Both numerical and observational data exhibit an increase in angle variability with increasing stratification, which seemingly indicates that the variability is related to physical processes of the flow, such as intermittency or laminarization/bursting phenomena. In the future, large-eddy simulation surface boundary conditions will need to better capture this variability to properly represent instantaneous land-surface interactions in the SBL.