Diffuse $gamma$-ray emission produced by the interaction of cosmic-ray particles with matter and radiation in the Galaxy can be used to probe the distribution of cosmic rays and their sources in different regions of the Galaxy. With its large field of view and long observation time, the Milagro Gamma Ray Observatory is an ideal instrument for surveying large regions of the Northern Hemisphere sky and for detecting diffuse $gamma$-ray emission at very high energies. Here, the spatial distribution and the flux of the diffuse $gamma$-ray emission in the TeV energy range with a median energy of 15 TeV for Galactic longitudes between 30$^circ$ and 110$^circ$ and between 136$^circ$ and 216$^circ$ and for Galactic latitudes between -10$^circ$ and 10$^circ$ are determined. The measured fluxes are consistent with predictions of the GALPROP model everywhere except for the Cygnus region ($lin[65^circ,85^circ]$). For the Cygnus region, the flux is twice the predicted value. This excess can be explained by the presence of active cosmic ray sources accelerating hadrons which interact with the local dense interstellar medium and produce gamma rays through pion decay.
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