When he's not in full Templar regalia, he wears a leather 'open faced' brigandine- that is, the armor plates are on the outside, whereas a closed-face would have the armor plates behind the leather facing. I couldn't speak to the historicity of that piece, there's speculation that it could be purely fictional (the Varangian Guardsmen wore something similar, but it had steel plates laced to the outside of the leather garment, as opposed to the leather plates Purefoy's character is wearing. When in full Templar regalia, he wears a full hauberk under the leather brigandine and an unattached coif underneath what appears to be a Pembridge style (or great helm perhaps, its been a while) helm.