Theresa,
You can accomplish this by doing two things. First, use the GP tool Calculate Locations which in addition to computing the network locations, also adds a field called Distance with the distance of the point to the network. When you do this, make sure the data is projected so that you do not get the distance in decimal degrees.
Second, let's assume that you are solving on Miles and the Distance field has been populated in miles as above.
Create a Route Layer and use Load Location to load the points. The Use Network Location Fields will be selected automatically and in the Location Analysis Properties, for the Attr_Miles (or what ever your impedance attribute name is), for the default value, click on the colum to get a drop down list of available attribute and choose Distance. Now when you click ok to load the locations, it will have mapped the off road distance to the Attr_Miles. Now solve. And the resulting path length will be the addition of the off road distance and the shortest path length.
Jay Sandhu