Sorry I do not know about this style. Nicely decorated!
Here is some information for you:
Images here: http://www.bing.com/images/search?q=italianate+1885&qpvt=italianate+1885&FORM=IGRE


More here: http://www.wentworthstudio.com/historic-styles/italianate

it looks like an early simple four square. four squares have 4 rooms downstairs and upstairs and were popular from 1890 to 1940.

maybe it's a two square.

This looks like an American Four Square, though interestingly, it doesn't have the front-facing dormer characteristic of these homes. Typically, Four Squares have two or more evenly spaced windows on the front elevation of the second floor. The first floor front elevation door and windows are also fairly evenly spaced, but not necessarily matching the placement of the second story. It appears that the front elevation of your home was altered at some point, replacing the front elevation second floor windows with a single centered one. It's possible the first floor was changed too, but I can't tell for sure. A good place to start with your exterior design would be to re-establish a more typical window pattern on the second floor. Even better if you can find evidence of their location by pulling back some of the siding. Here's a good resource for photos of Four Squares across the US:
http://www.oldhouseweb.com/architecture-and-design/american-foursquare-1890-1930.shtml