We present a new implicit method for the solution of the compressible Navier-Stokes equations on hybrid unstructured finite-volume meshes. The solver combines line relaxation and the matrix-based point relaxation methods for time integration. In general, the line relaxation method is used in layers of hexahedral or prismatic cells near solid surfaces, and the point relaxation method is used in the remainder of the domain. This results in a method that combines the rapid convergence of a line-relaxation implicit method with the flexibility of using unstructured grids to represent complex geometries. Initial results on blunt body flows indicate that the combined line and point relaxation method has a somewhat degraded convergence rate compared to a pure line-relaxation method. However, the results are encouraging and show that the method will be useful for the simulation of complex geometry hypersonic flows. With the present implementation of the flux evaluation on tetrahedral finite volumes, we were unable to obtain accurate heat transfer predictions unless the bow shock was captured using a region of hexahedra. Thus, good grid design is still required to obtain high quality results using unstructured grids.