Furnace vent in chase with fireplace chimney - OK?

[AHI in AR]

I looked at a house yesterday which had a typical manufactured fireplace enclosed in a wood sided chase running up two stories. The furnace and water heater in the crawlspace combined into a single B-vent, and they used the dead space in the fireplace chimney chase to run the vent up. It exited adjacent to the chimney underneath the same large cap. This seems like a bad idea to me, but I'm not aware that there is any actual code prohibition against it. Anybody know?