If you mediate my divorce, can't you just file in court for us since you are also a lawyer?

No. If I am acting as a mediator for you and your spouse, I cannot also act as a lawyer. I believe it to be a huge but indirect advantage in mediation that I am also an Illinois divorce lawyer. That being said, however, it would be wrong to give legal advice in mediation sessions. By the same token, it is a conflict of interest for a mediator to then file legal documents (in your case if you live in Illinois, your Petition for Dissolution of Marriage) on behalf of someone who received their mediation services. Your mediator will prepare a Memorandum that will go to your lawyers documenting everything that was agreed upon. 

You may also be wondering about why it may be a good idea to have a mediator even if you already have a lawyer trying to negotiate your divorce.