OP, I think the most important question is: on your current commute with the MTB, are you running out of gears in either direction? I.e. going up hills do you get down to the granny combination (chain all the way to the left) and still can't pedal at smooth, brisk cadence of, say 80+rpm? Going down hills, do you get into the high combination (chain all the way to the right) and still spin out? (And if you do spin out, do you care, or are you content to roll downhill plenty fast?)
If your existing gear range is working for you (and will continue to work on the new commute) then I"d say you do not need a new bike, you are fine as is. (Of course, new bikes are fun! So if you have money to buy one, buy one! Maybe do you have cyclist friends that could loan you bikes to try out and see what you like?)
The other consideration mentioned above is about suspension fork. If you have to stand on the pedals going uphill you will bounce like crazy and lose tons of energy. And even if you don't stand up, you will bounce some, and lose some energy. So if your fork has "lockout", use it. If not, you might consider a new bike, or at least a rigid fork or a fork with lockout.
As many have recommended above, "cyclocross" is the keyword to look for in a road bike. Essentially, it is a kind of road bike, and among the many types of road bikes it is the most robust for commuting while still offering some performance. I commute on a Crosscheck (like some of those above), and I love it; but there are other models that would work as well. Also somebody mentioned carrying their bike up and down stairs; one peculiarty of cyclocross bikes is they are designed with the rear brake cable is routed along the top of the top tube, so it can be more comfortably carried on your shoulder.
Another option would be a "touring" bike, but that design is oriented towards carrying heavy loads long distances at low speeds (think bike-camping). Get a tourer if you want to feel like you're driving a bus.
Stay away from "hybrids" as well, unless you want to feel like you're a bear riding a bike in a circus.