James has done them that way too.
If you design the bow to take advantage of the compression strength of the horn plus the tension strength of the sinew it should shoot similar to the Asiatic bows. If it is too long or has too much mass the horn and sinew become liabilities. I think a Molle style bow would be a good candidate for horn/sinew and I believe a few have been presented right here on PA.
There are a few Native American Plains style bows that were a combo of sinew/wood/horn or sinew/horn or just plain ole' sinew/wood bows.
Over the last few years a few commercial bowyers have put horn bellies on their boo backed bows and maybe even glass backed bows. For me, you need a short, highly stressed bow before horn and/or sinew comes into the picture.