For a ride of 1.5 miles, starting and ending indoors, you can get by easily with your current list of clothing. Only thing I would add would be some light rain pants to keep your jeans from being getting totally soaked and then having to sit in class like that for hours after a really wet ride. I'm always amazed how quickly I get wet right through during a heavy rain, if I don't have rain gear.

For longer rides, you'll want clothing that will be comfortable during long stretches of bad weather, and it sounds like you've got that covered. There was a time when I would go outside in anything. There was one camping trip where I woke up to find my pants so frozen I had to punch them into shape with my fists to get them on, and thought nothing of it.