  We present detections of 21-cm emission from neutral hydrogen (HI) in the
circumgalactic medium (CGM) of the local edge-on galaxies NGC 891 and NGC 4565
using the Robert C. Byrd Green Bank Telescope (GBT). With our 5$\sigma$
sensitivity of $8.2 \times 10^{16}$ cm$^{-2}$ calculated over a 20 km s$^{-1}$
channel, we achieve $>5\sigma$ detections out to $90-120$ kpc along the minor
axes. The velocity width of the CGM emission is as large as that of the disk
$\approx 500$ km s$^{-1}$, indicating the existence of a diffuse component
permeating the halo. We compare our GBT measurements with interferometric data
from the Westerbork Synthesis Radio Telescope (WSRT). The WSRT maps the HI
emission from the disk at high S/N but has limited surface brightness
sensitivity at the angular scales probed with the GBT. After convolving the
WSRT data to the spatial resolution of the GBT (FWHM = 9.1$'$), we find that
the emission detected by the WSRT accounts for $48^{+15}_{-25}$%
($58^{+4}_{-18}$%) of the total flux recovered by the GBT from the CGM of NGC
891(NGC 4565). The existence of significant GBT-only flux suggests the presence
of a large amount of diffuse, low column density HI emission in the CGM. For
reasonable assumptions, the extended diffuse HI could account for $5.2\pm0.9$%
and $2.0\pm0.8$% of the total HI emission of NGC 891 and NGC 4565.
