Separating Servicemember Handbook Development Act - Amends the National Defense Authorization Act for Fiscal Year 2008 to direct the Secretary of Defense to develop and maintain, in a handbook and on a publically-available Internet website, a comprehensive description of the compensation and other benefits to which an Armed Forces member, and the family of the member, would be entitled on separation or retirement resulting from a serious injury or illness. Requires that the handbook be provided to each member as soon as practicable following an injury or illness for which the member may retire or separate.