We actually spent a good amount of time learning the exact definitions of this kind of stuff in the gen chem class I just took.
A "mixture" can be homogenous or heterogenous. If the entire mixture is in a single phase, however, it is considered homogenous. So, in a homogenous mixture you would expect every property to be the same throughout.
It looks like you guys already have this figured out, but I thought I might as well add that in just in case it helps.