If you have 9.3, then you can use the following VBA and run it after you solve the Closest Facility. It will add two new feature classes representing the lines and junctions that were traversed.
Regards,
Jay Sandhu
Public Sub AddNATraversalResultToArcMap()
Dim pMxDoc As IMxDocument
Dim pNetworkAnalystExtension As INetworkAnalystExtension
Dim pNALayer As INALayer
Dim pFLayer As IFeatureLayer
Dim pTraversalResultQuery As INATraversalResultQuery
Dim pNATraversalResultEdit As INATraversalResultEdit
Set pMxDoc = ThisDocument
Set pNetworkAnalystExtension = Application.FindExtensionByName("Network Analyst")
Set pNALayer = pNetworkAnalystExtension.NAWindow.ActiveAnalysis
Set pTraversalResultQuery = pNALayer.Context.Result
Set pNATraversalResultEdit = pTraversalResultQuery
'Infer Geometry
pNATraversalResultEdit.InferGeometry "", Nothing, New CancelTracker
'Get the Edges and add as a layer
Set pFLayer = New FeatureLayer
Set pFLayer.FeatureClass = pTraversalResultQuery.FeatureClass(esriNETEdge)
pFLayer.Name = pFLayer.FeatureClass.AliasName
pMxDoc.FocusMap.AddLayer pFLayer
'Get the Junctions and add as a layer
Set pFLayer = New FeatureLayer
Set pFLayer.FeatureClass = pTraversalResultQuery.FeatureClass(esriNETJunction)
pFLayer.Name = pFLayer.FeatureClass.AliasName
pMxDoc.FocusMap.AddLayer pFLayer
End Sub