I found the solution with help from Kean Walmsley.
The following code works:
AddHandler AcApp.DocumentManager.DocumentActivated, AddressOf Me.DocumentManager_DocumentActivated
...
Private Sub DocumentManager_DocumentActivated(ByVal sender As Object, ByVal e As DocumentCollectionEventArgs)
If Application.DocumentManager.MdiActiveDocument IsNot Nothing Then
MsgBox("Active drawing has changed!")
End If
End Sub