Basta definire questa nuova classe ed usarla al posto di String:
codice:
Public Class ListElement
    Private m_text As String
    Private m_id As Integer

    Public Property Text() As String
        Get
            Return m_text
        End Get
        Set(ByVal Value As String)
            m_text = Value
        End Set
    End Property

    Public Property ID() As Integer
        Get
            Return m_id
        End Get
        Set(ByVal Value As Integer)
            m_id = Value
        End Set
    End Property

    Public Sub New(ByVal text As String, ByVal id As Integer)
        m_text = text
        m_id = id
    End Sub

    Public Overrides Function ToString() As String
        Return m_text
    End Function
End Class

'nella parte che carica il Combo:
Dim le As ListElement

While objReader.Read
    le = New ListElement(objReader("Comune"), objReader("ID"))
    cmbBoxComune.Items.Add(le)
End While

'in seguito, per conoscere l'ID selezionato nel combo:
Private Sub cmbBoxComune_SelectedIndexChanged(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles cmbBoxComune.SelectedIndexChanged
    Dim le As ListElement

    le = CType(cmbBoxComune.SelectedItem, ListElement)

    Console.WriteLine(co.ID)
End Sub