An old graphic created for the The SciFi Vine Jade family (almost certainly by Erin Kyan)
House Jade is one of many Terrareen Hunter Houses, one of many, that raises girls as monster hunters. House Jade, or at least Jaina Jade and Pasht's local branch, seems to specialize in vampires.
No current House Jade members are known in Ree's canon, although the possibility exists that Amber Glass, despite her name, may be a late recruit. If she is part of House Jade (rather than House Glass, as her name suggests), she would have grown up mostly or entirely apart from the House, which would make her very different from Jaina.
Cate Whitlen is probably a House member from further down the timeline.
Reality
The House of Jade (and similar terminology) were also labels for the Jade family of Cloud City at The SciFi Vine. This Jade family was headed by Ree, in the guise of Jaina Jade.