Depends on the climate in my honest opinion. I would not support steel with timber in a garage in Canada (where you'd have the potential for pretty large differences in temperature over time, as well as lots of cyclical wet/dry and high to low moisture levels in addition to chemical attack possibilities), but often do so here in New Zealand. The combination of climate and climate specific timber treatment options here permit this type of construction.
Just as an aside, when detailing steel posts for steel beams you can create problems with differential shrinkage , just like Mike talked about, as well as the different coefficients of thermal expansion. Detailing can solve much of these, and essentially I use pin connections and ensure that my detailing permits some rotation.
Cheers,
YS
B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...