How do we know that we are NOT in an "Ice Age?"
I think you're slightly confused by some of the terminology. (Caveat: I'm a geophysist, take anything I say with a grain of salt!)

We're currently in an interglacial during a prolonged period of icehouse climate (most of the Cenozoic). 

During most of the Earth's history, the overall climate tends to be much warmer and more stable on the million-year scale. These periods are referred to as "greenhouse" climates.  During these times, there's relatively little evidence for extensive ice sheets (either on continents or over the ocean) at the poles.  

However, during times of "icehouse" climate, the Earth becomes cooler.  Ice masses develop at the poles and due to regular preturbations in Earth's orbit (Milankovich cycles), continental ice sheets tend to advance and retreat.  (Assuming there are continents near the poles.)  This leads to regular glacial and interglacial periods.

Presumably, regular fluctuations in climate due to Milankovich cycles would occur during periods of greenhouse climate.  However, ice sheets cause positive feedback that amplifies the effect of the Milankovich cycles.  This is largely due to ice and snow's albedo: they reflect more sunlight back into space instead of adsorbing it.  Therefore greenhouse Milankovich cycles were probably smaller.  (There's probably a lot more to the story. I'm not an ideal person to ask.)