Forgive and forget?

Melissa and I were watching TV and someone on the show said to another character "I'll forgive you, but I will never forget what you did." Melissa replied, "We'll then He's not really forgiving her." This sparked a whole conversation on forgiving and forgetting, and now it is on my mind. Looking to the bible for answers I found lots on forgiveness. The most helpful passages I found were about striving to be like Christ when forgiving. We should use him as a model when we forgive others. Now when Christ forgives us he forgets that we ever sinned. He can do this because he is God. But I can't. I can forgive people and not hold their sins against them, or not be angry with them, but sometimes I don't completely forget them. I still remember situations and events in which someone sinned against me, but I think that is okay as long as I am not still bitter about it. So Melissa and I came to the conclusion that you can forgive someone and not forget what they did as long as you are not remembering with the wrong attitude.....maybe we are wrong though. If we are someone tell me.