This type of gown and headgear, including the same colour choices seem to have been very popular in the Low countries and possibly even France in the 1560s-70s. There are quite a few examples to be seen in the dress diary.
Another example of this exact type of gown can be seen in this painting from the famous Calvinist temple in Lyon, in 1565. The woman entering from the left wears the black gown without the black partlet, and her veil pinned on her cap is smaller. Still they are very alike.
Anyway, to say something about the gown, for those who won't check out the dress diary: The innermost layer is as always a smock, this one is high necked. Then I wear a lightly boned kirtle made from wool. The black gown is made from a worsted tabby and wholly lined in the same fabric. The guards are from black wool cloth and so is the partlet, which is lined in self patterned white linen (variations of stripes). The partlet is buttoned with pewter buttons.
The red sleeves, which tie to the kirtle, are made from silk and lined in linen. They have a curved shape taken from several sleeves in Janet Arnold's Patterns of Fashion. When the pictures were taken I also wore a matching red silk pettiocat, to look more like the woman in the painting from Lyon.
The headwear is a linen cap with a lace "brim" and a wired, starched linen veil pinned on top of it. Since what people really want to do at a costuming site is to look at pretty pictures there are more of them below, click on them to get a bigger picture: In the middle photo you can almost work out how the veil is pinned ;) If you want to know more about how this dress was constructed, go check out the dress diary! Do look at it, it has lots of research among the trials of sewing.