I would say no, it is only a hydrogen bond, not a halogen bond.
To be a halogen bond, the halogen atom must accept electron density from the other member of the bond. If the other member of the bond is a hydrogen atom bonded to a more electronegative element, I don't see have the halogen atom could be an acceptor of electron density.
If you can get access see "Halogen Versus Hydrogen" Science Vol. 321 no. 5891 pp. 918-919. Footnote 7 there explains: "A halogen bonding donor is a species that contains an electrophilic halogen that can become a member of a halogen bond. In the literature on halogen bonding, the reader should be alert to how the words 'donor' and 'acceptor' are used. In a complex RX---B, RX is the halogen bond donor but the electron acceptor (Lewis acid); B is the electron donor and halogen bond acceptor (Lewis base)."