That's a good question, EvLer. The input circuit for traditional CMOS devices is pretty symmetric, and hence the actual switching point is pretty close to mid-rail. The CMOS gate actually goes into a linear mode when the input is near mid-rail, so you generally don't want to keep a CMOS input near mid-rail for long, or the Idd for the part will go up a fair amount. There are times when you run a CMOS gate in linear mode, but those are tricks outside the scope of normal digital logic.
The 1.5V and 3.5V threasholds listed in the datasheets for CMOS logic's Vil and Vih are there to provide voltage margin, not to reflect the actual switching voltages. If you test and plot Vo versus Vi for a CMOS gate, you will see that the switchover of the output occurs pretty close to when the input voltage passes through half of Vdd. The Vih and Vil levels for regular CMOS logic are listed away from the mid-rail switching point so that the logic that drives the CMOS input is ensured to have a good wide drive capability, and to ensure that the CMOS gate is kept away from its linear (higher Idd) mode of operation.
Schmidt input gates have hysteresis feedback built in, so that the gate can be driven with a slow analog waveform and the gate won't stall in the linear mid-range of the supply. For example, if you want to have a slow R-C relaxation oscillator with a CMOS gate as the active component, you need to use a Schmidt trigger inverter. You would connect the output of the inverter through a resistor to the input of the gate, and connect a capacitor from the input to ground. The period of oscillation is close to the R-C time constant, with some adjustments.
Vih and Vil numbers make less sense to publish for Schmidt input gates, because what you care about is what the hysteresis voltage is, and the + and - trip voltages are generally centered around mid-rail (with some tolerance). If you are driving a Schmidt input gate with other logic, you still want to treat it as a CMOS input and drive it with good CMOS levels. If you are using the Schmidt input gate for a more analog function or to handle slowly-changing input waveforms, then you will generally treat it more as an analog input and use the trip voltages in your margin calculations.
Hope that helps. -Mike-