http://www.talktomeinkorean.com/lessons/level-2-lesson-24/ Listen to this lesson. According to this lesson the difference is as follows: """ The difference between 이미 and 벌써 lies in whether you are already aware of the fact or not. When you and/or the speaker know about something already and talk about it, you use 이미. When you are just finding out about it as you speak you use 벌써. People don’t always stick to this rule, but this is the basic idea. """

You are right. the two words mean "already" and can be used interchangeably. Sometimes, we use the two words together to stress the tone as in the below example (3). ex) I already knew that you would be dumped by her. (1) 난 너가 그 여자한테 차일 줄 이미 알고 있었다. (2) 난 너가 그 여자한테 차일 줄 벌써 알고 있었다. (3) 난 너가 그 여자한테 차일 줄 이미 벌써 알고 있었다.