Coronal holes (CHs) are regions with unbalanced magnetic flux and have been associated with open magnetic field (OMF) structures. However, it has been reported that some CHs do not intersect with OMF regions. To investigate the inconsistency, we apply a potential-field (PF) model to construct the magnetic fields of the CHs. As a comparison, we also use a thermodynamic magnetohydrodynamic (MHD) model to synthesize coronal images and identify CHs from the synthetic images. The results from both the potential-field CHs and synthetic MHD CHs reveal that there is a significant percentage of closed field lines extending beyond the CH boundaries and more than 50% (17%) of PF (MHD) CHs do not contain OMF lines. The boundary-crossing field lines are more likely to be found in the lower latitudes during active times. While they tend to be located slightly closer than the non-boundary-crossing ones to the CH boundaries, nearly 40% (20%) of them in PF (MHD) CHs are not located in the boundary regions. The CHs without open field lines are often smaller and less unipolar than those with open field lines. The MHD model indicates higher temperature variations along the boundary-crossing field lines than the non-boundary-crossing ones. The main difference between the results of the two models is that the dominant field lines in the PF and MHD CHs are closed and open field lines, respectively.