If I write a contract between myself and my separating spouse concerning the division of our assets, and it is signed by both parties, is it legally binding?

I do not practice family law in Virginia.  As a result, I only deal with Maryland divorce laws.  So, be aware that this answer is coming from a divorce lawyer in Maryland.

Having said that, it is my understanding that practically ever state will allow a written agreement signed by both spouses to become legally binding.  So that there are no issues over whether the document was forged, make sure both you and your souse sign before a notary, and the notary notarizes the signatures.  The contract should describe the terms of your agreement with particularity and detail.  In other words, do not just say "husband gets the tv", but instead say "husband gets the [X] inch [make model year] plasma television that was located in the master bedroom of [address] on [date], see wife's [date] picture taken on her [describe camera or phone that took the picture]."  In otherwords, the more detail the better.

Now, if there is only one television, then you may need less detail.  However, esepcially with parties that do not have a lawyer, the more detail the better, out of an abundance of caution.  You should still consult with a licensed family attorney in your state.